Intrinsic Viscosity of Polymers: General Theory Based on a Partially Permeable Sphere Model

Star-PCL shape memory polymer (SMP) scaffolds with tunable transition temperatures for enhanced utility

Thermoresponsive shape memory polymers (SMPs) prepared from UV-curable poly(ε-caprolactone) (PCL) macromers have the potential to create self-fitting bone scaffolds, self-expanding vaginal stents, and other shape-shifting devices. To ensure tissue safety during deployment, the shape actuation temperature (i.e., the melt transition temperature or Tm of PCL) must be reduced from ∼55 °C that is observed for scaffolds prepared from linear-PCL-DA (Mn ∼ 10 kg mol-1). Moreover, increasing the rate of biodegradation would be advantageous, facilitating bone tissue healing and potentially eliminating the need for stent retrieval. Herein, a series of six UV-curable PCL macromers were prepared with linear or 4-arm star architectures and with Mns of 10, 7.5, and 5 kg mol-1, and subsequently fabricated into six porous scaffold compositions (10k, 7.5k, 5k, 10k★, 7.5k★, and 5k★) via solvent casting particulate leaching (SCPL). Scaffolds produced from star-PCL-tetraacrylate (star-PCL-TA) macromers produced pronounced reductions in Tm with decreased Mnversus those formed with the corresponding linear-PCL-diacrylate (linear-PCL-DA) macromers. Scaffolds were produced with the desired reduced Tm profiles: 37 °C < Tm < 55 °C (self-fitting bone scaffold), and Tm ≤ 37 °C (self-expanding stent). As macromer Mn decreased, crosslink density increased while % crystallinity decreased, particularly for scaffolds prepared from star-PCL-TA macromers. While shape memory behavior was retained and radial expansion pressure increased, this imparted a reduction in modulus but with an increase in the rate of degradation.

Carboxymethyl hydroxypropyl guar gum physicochemical properties in dilute aqueous media

We investigate carboxymethyl hydroxypropyl guar gum (CMHPG) solution properties in water and NaCl, KCl, and CaCl2 aqueous solutions. The Huggins, Kraemer, and Rao models were applied by fitting specific and relative viscosity of CMHPG/water and CMHPG/salt/water to determine the intrinsic viscosity [η]. The Rao models yielded better results (R2 = 0.779-0.999) than Huggins and Kraemer equations. [η] decreased up to 84% in salt solution over the range 0.9-100 mM compared to water. Salt effects screened the CMHPG charged side groups chains leading to a compacted structure. In 0.9 mM NaCl(aq), the hydrodynamic coil radius (Rcoil) was 28% smaller and 45% smaller in 100 mM NaCl solution relative to water. Similar decreases were seen in KCl and CaCl2 solutions. KCl and CaCl2 were more effective than NaCl. CMHPG is salt-tolerant and shows comparatively less viscosity change than native guar gum, with modest reduced viscosity increases with CMHPG dilution at all salt concentrations. The electrostatic interactions were effective up to 100 mM salt. The activation energy of viscous flow for CMHPG solutions was computed and compared to measured xanthan gum and several literature values. These data show that the barrier to CMHPG flow is higher than for xanthan gum.

Mechanism for gel formation of pectin from mealy and crisp lotus rhizome induced by Na+ and D-glucono-d-lactone

Lotus rhizome residue, a cell wall material produced during the production of lotus rhizome starch, has long been underutilized. This study aims to extract pectin-rich polysaccharides from the cell wall of lotus rhizome and investigate their gelation mechanism in order to improve their industrial applicability. The results indicated that both CP and MP (pectin extracted from crisp and mealy lotus rhizome) exhibited a highly linear low methoxyl pectin structure, with the primary linkage mode being →4)-GalpA-(1→. The pectin chains in MP were found to be more flexible than those in CP. Then the impact of Na+, D-glucono-d-lactone (GDL), urea, sodium dodecyl sulfate (SDS), either individually or in combination, on the rheological characteristics of gels was evaluated. The results indicated that gels induced by GDL exhibited favorable thermoreversible properties, whereas the thermoreversibility of Na+-induced gels is poor. In addition to hydrogen bonding and ionic interactions, hydrophobic interactions also play a significant role in the formation of pectin gels. This study offers theoretical guidance and methodologies to improve the utilization rate of lotus rhizome starch processing by-products, while also provides novel insights into the correlation between LMP structure and gelation mechanism.

Salt and Temperature Effects on Xanthan Gum Polysaccharide in Aqueous Solutions

Xanthan gum (XG) is a carbohydrate polymer with anionic properties that is widely used as a rheology modifier in various applications, including foods and petroleum extraction. The aim was to investigate the effect of Na+, K+, and Ca2+ on the physicochemical properties of XG in an aqueous solution as a function of temperature. Huggins, Kraemer, and Rao models were applied to determine intrinsic viscosity, [η], by fitting the relative viscosity (ηrel) or specific viscosity (ηsp) of XG/water and XG/salt/water solutions. With increasing temperature in water, Rao 1 gave [η] the closest to the Huggins and Kraemer values. In water, [η] was more sensitive to temperature increase (~30% increase in [η], 20-50 °C) compared to salt solutions (~15-25% increase). At a constant temperature, salt counterions screened the XG side-chain-charged groups and decreased [η] by up to 60% over 0.05-100 mM salt. Overall, Ca2+ was much more effective than the monovalent cations in screening charge. As the salt valency and concentration increased, the XG coil radius decreased, making evident the effect of shielding the intramolecular and intermolecular XG anionic charge. The reduction in repulsive forces caused XG structural contraction. Further, higher temperatures led to chain expansion that facilitated increased intermolecular interactions, which worked against the salt effect.

Step-growth polymerization by the RAFT process

Reversible Addition-Fragmentation Chain Transfer (RAFT) step-growth polymerization is an emerging method that synergistically combines the benefits of RAFT polymerization (functional group and user-friendly nature) and step-growth polymerization (versatility of the polymer backbone). This new polymerization method is generally achieved by using bifunctional reagents of monomer and Chain Transfer Agent (CTA), that efficiently yield Single Monomer Unit Insertion (SUMI) adducts under stoichiometrically balanced conditions. This review covers a brief history of the RAFT-SUMI process and its transformation into RAFT step-growth polymerization, followed by a comprehensive discussion of various RAFT step-growth systems. Furthermore, characterizing the molecular weight evolution of step-growth polymerization is elaborated based on the Flory model. Finally, a formula is introduced to describe the efficiency of the RAFT-SUMI process, assuming rapid chain transfer equilibrium. Examples of reported RAFT step-growth and SUMI systems are then categorized based on the driving force.

New Facet in Viscometry of Charged Associating Polymer Systems in Dilute Solutions

The peculiarities of viscosity data treatment for two series of polymer systems exhibiting associative properties: brush-like amphiphilic copolymers-charged alkylated N-methyl-N-vinylacetamide and N-methyl-N-vinylamine copolymer (MVAA-co-MVAC_nH_2n+1) and charged chains of sodium polystyrene-4-sulfonate (PSSNa) in large-scale molecular masses (MM) and in extreme-scale of the ionic strength of solutions were considered in this study. The interest in amphiphilic macromolecular systems is explained by the fact that they are considered as micellar-forming structures in aqueous solutions, and these structures are able to carry hydrophobic biologically active compounds. In the case of appearing the hydrophobic interactions, attention was paid to discussing convenient ways to extract the correct value of intrinsic viscosity η from the combined analysis of Kraemer and Huggins plots, which were considered as twin plots. Systems and situations were demonstrated where intrachain hydrophobic interactions occurred. The obtained data were discussed in terms of lnηr vs. cη plots as well as in terms of normalized scaling relationships where ηr was the relative viscosity of the polymer solution. The first plot allowed for the detection and calibration of hydrophobic interactions in polymer chains, while the second plot allowed for the monitoring of the change in the size of charged chains depending on the ionic strength of solutions.

Fabrication of Double-Stranded Vinyl Polymers Mediated by Coordination Nanochannels

Although double-stranded structures are commonly found in biopolymers, a general and versatile methodology for fabricating double-stranded synthetic polymers has not yet been developed. Here, we report a new approach for synthesizing double-stranded polymers composed of polystyrene and poly(methyl methacrylate). We conducted crosslinking radical polymerization inside a metal-organic framework (MOF), which had one-dimensional channels with diameters similar to the thickness of two polymer chains. Effective spatial constraint within the MOF pores facilitated highly regulated crosslinking reactions between two polymer chains with extended conformations. Remarkably, the obtained double-stranded polymers were soluble in many organic solvents, even at a high crosslinking ratio (20%), unlike conventional crosslinked polymers. Notably, this stable duplex topology, which was inaccessible using previous methods, endowed the double-stranded vinyl polymers with unusual properties in the solution and bulk states. By designing the properties of the MOF nanochannels, the proposed technique can contribute to the development of a wide range of synthetic polymer duplexes.

Dynamical and Structural Properties of Comb Long-Chain Branched Polymer in Shear Flow

Using hybrid multi-particle collision dynamics (MPCD) and a molecular dynamics (MD) method, we investigate the effect of arms and shear flow on dynamical and structural properties of the comb long-chain branched (LCB) polymer with dense arms. Firstly, we analyze dynamical properties of the LCB polymer by tracking the temporal changes on the end-to-end distance of both backbones and arms as well as the orientations of the backbone in the flow-gradient plane. Simultaneously, the rotation and tumbling behaviors with stable frequencies are observed. In other words, the LCB polymer undergoes a process of periodic stretched–folded–stretched state transition and rotation, whose period is obtained by fitting temporal changes on the orientation to a periodic function. In addition, the impact induced by random and fast motions of arms and the backbone will descend as the shear rate increases. By analyzing the period of rotation behavior of LCB polymers, we find that arms have a function in keeping the LCB polymer’s motion stable. Meanwhile, we find that the rotation period of the LCB polymer is mainly determined by the conformational distribution and the non-shrinkable state of the structure along the velocity-gradient direction. Secondly, structural properties are numerically characterized by the average gyration tensor of the LCB polymer. The changes in gyration are in accordance with the LCB polymer rolling when varying the shear rate. By analyzing the alignment of the LCB polymer and comparing with its linear and star counterparts, we find that the LCB polymer with very long arms, like the corresponding linear chain, has a high speed to reach its configuration expansion limit in the flow direction. However, the comb polymer with shorter arms has stronger resistance on configuration expansion against the imposed flow field. Moreover, with increasing arm length, the comb polymer in shear flow follows change from linear-polymer-like to capsule-like behavior.

Influence of network defects on the conformational structure of nanogel particles: From "closed compact" to "open fractal" nanogel particles

We propose an approach to generate a wide range of randomly branched polymeric structures to gain general insights into how polymer topology encodes a configurational structure in solution. Nanogel particles can take forms ranging from relatively symmetric sponge-like compact structures to relatively anisotropic open fractal structures observed in some nanogel clusters and in some self-associating polymers in solutions, such as aggrecan solutions under physiologically relevant conditions. We hypothesize that this broad "spectrum" of branched polymer structures derives from the degree of regularity of bonding in the network defining these structures. Accordingly, we systematically introduce bonding defects in an initially perfect network having a lattice structure in three and two topological dimensions corresponding to "sponge" and "sheet" structures, respectively. The introduction of bonding defects causes these "closed" and relatively compact nanogel particles to transform near a well-defined bond percolation threshold into "open" fractal objects with the inherent anisotropy of randomly branched polymers. Moreover, with increasing network decimation, the network structure of these polymers acquires other configurational properties similar to those of randomly branched polymers. In particular, the mass scaling of the radius of gyration and its eigenvalues, as well as hydrodynamic radius, intrinsic viscosity, and form factor for scattering, all undergo abrupt changes that accompany these topological transitions. Our findings support the idea that randomly branched polymers can be considered to be equivalent to perforated sheets from a "universality class" standpoint. We utilize our model to gain insight into scattering measurements made on aggrecan solutions.

Reversible Addition-Fragmentation Chain Transfer Step-Growth Polymerization with Commercially Available Inexpensive Bis-Maleimides

Here, commercially available N-aromatic substituted bismaleimides were used in RAFT step-growth polymerization for the first time. In our initial report (J. Am. Chem. Soc. 2021, 143 (39), 15918-15923), maleimide precursors...

Structure-dilute solution property relationships of comb-like macromolecules in a good solvent

The structural characterization of branched polymers still poses experimental challenges despite their technological potential. This lack of clarity is egregious in linear low-density polyethylene (LLDPE), a common industrial plastic. Here, we design a coarse-grain, implicit solvent molecular dynamics model for LLDPE in 1,2,4-trichlorobenzene, a canonical good solvent, that replicates all-atom simulations and experiments. We employ this model to test the relationship between the contraction factors, the ratios of branched to linear dilute solution properties. In particular, we relate the contraction factor of the radius of gyration to that of the intrinsic viscosity and the hydrodynamic radius. The contraction exponents are constant as we vary branch length and spacing in contrast to theoretical expectations. We use this observation to develop a general theory for the dilute solution properties of linear polymers with linear side-chain branches, comb-like macromolecules, in a good solvent and validate the theory by generating master curves for LLDPE.

Structure and conformational properties of ideal nanogel particles in athermal solutions

We investigate the conformational properties of "ideal" nanogel particles having a lattice network topology by molecular dynamics simulations to quantify the influence of polymer topology on the solution properties of this type of branched molecular architecture. In particular, we calculate the mass scaling of the radius of gyration (Rg), the hydrodynamic radius, as well as the intrinsic viscosity with the variation of the degree of branching, the length of the chains between the branched points, and the average mesh size within these nanogel particles under good solvent conditions. We find competing trends between the molecular characteristics, where an increase in mesh size or degree of branching results in the emergence of particle-like characteristics, while an increase in the chain length enhances linear polymer-like characteristics. This crossover between these limiting behaviors is also apparent in our calculation of the form factor, P(q), for these structures. Specifically, a primary scattering peak emerges, characterizing the overall nanogel particle size. Moreover, a distinct power-law regime emerges in P(q) at length scales larger than the chain size but smaller than Rg of the nanogel particle, and the Rg mass scaling exponent progressively approaches zero as the mesh size increases, the same scaling as for an infinite network of Gaussian chains. The "fuzzy sphere" model does not capture this feature, and we propose an extension to this popular model. These structural features become more pronounced for values of molecular parameters that enhance the localization of the branching segments within the nanogel particle.

Reversible-Addition Fragmentation Chain Transfer Step-Growth Polymerization

Reversible-addition fragmentation chain transfer (RAFT) polymerization has been widely explored since its discovery due to its structural precision, versatility, and efficiency. However, the lack of tunability of the polymer backbone limits some applications. Herein, we synergistically combine RAFT and step-growth polymerization mechanisms, by employing a highly selective insertion process of a single monomer with a RAFT agent, to achieve RAFT step-growth polymerization. A unique feature of the RAFT step-growth polymers is that each backbone repeat unit bears a pendant RAFT agent, which can subsequently graft side chains in a second polymerization step and afford molecular brush polymers. Enabled by cleavable backbone functionality, we demonstrate transformation of the resulting brushlike polymers into linear chains of uniform size upon a stimulus.

Shape memory polymer (SMP) scaffolds with improved self-fitting properties

"Self-fitting" shape memory polymer (SMP) scaffolds prepared as semi-interpenetrating networks (semi-IPNs) with crosslinked linear-poly(ε-caprolactone)-diacrylate (PCL-DA, M_n∼10 kg mol^-1) and linear-poly(l-lactic acid) (PLLA, M_n∼15 kg mol^-1) [75/25 wt%] exhibited robust mechanical properties and accelerated degradation rates versus a PCL-DA scaffold control. However, their potential to treat irregular craniomaxillofacial (CMF) bone defects is limited by their relatively high fitting temperature (T_fit∼55 °C; related to the T_m of PCL) required for shape recovery (i.e. expansion) and subsequent shape fixation during press fitting of the scaffold, which can be harmful to surrounding tissue. Additionally, the viscosity of the solvent-based precursor solutions, cast over a fused salt template during fabrication, can limit scaffold size. Thus, in this work, analogous semi-IPN SMP scaffolds were formed with a 4-arm star-PCL-tetracryalate (star-PCL-TA) (M_n∼10 kg mol^-1) and star-PLLA (M_n∼15 kg mol^-1). To assess the impact of a star-polymer architecture, four semi-IPN compositions were prepared: linear-PCL-DA/linear-PLLA (L/L), linear-PCL-DA/star-PLLA (L/S), star-PCL-TA/linear-PLLA (S/L) and star-PCL-TA/star-PLLA (S/S). Two PCL controls were also prepared: LPCL (i.e. 100% linear-PCL-DA) and SPCL (i.e. 100% star-PCL-TA). The S/S semi-IPN scaffold exhibited particularly desirable properties. In addition to achieving a lower, tissue-safe T_fit (∼45 °C), it exhibited the fastest rate of degradation which is anticipated to more favourably permit neotissue infiltration. The radial expansion pressure exerted by the S/S semi-IPN scaffold at T_fit was greater than that of LPCL, which is expected to enhance osseointegration and mechanical stability. The intrinsic viscosity of the S/S semi-IPN macromer solution was also reduced such that larger scaffold specimens could be prepared.

Dendrimer Dynamics: A Review of Analytical Theories and Molecular Simulation Methods

The theoretical study of dendrimers is reviewed, considering both analytical approaches and molecular simulation methods. We discuss the effect of molecular symmetry on the degeneracy of the relaxation times, and then the calculation of observable quantities, in particular the intrinsic viscosity, and then the viscoelastic complex modulus and the dynamic structure factor, in comparison with the available experimental data. In particular, the maximum intrinsic viscosity with increasing molar mass is analyzed in some detail. The approximations and/or assumptions of the adopted methods are also described in connection with analogous results for polymer of a different topology, in particular linear and star polymers.

Dendrimers as Pharmaceutical Excipients: Synthesis, Properties, Toxicity and Biomedical Applications

The European Medicines Agency (EMA) and the Current Good Manufacturing Practices (cGMP) in the United States of America, define excipient as the constituents of the pharmaceutical form other than the active ingredient, i.e., any component that is intended to furnish pharmacological activity. Although dendrimers do not have a pharmacopoeia monograph and, therefore, cannot be recognized as a pharmaceutical excipient, these nanostructures have received enormous attention from researchers. Due to their unique properties, like the nanoscale uniform size, a high degree of branching, polyvalency, aqueous solubility, internal cavities, and biocompatibility, dendrimers are ideal as active excipients, enhancing the solubility of poorly water-soluble drugs. The fact that the dendrimer's properties are controllable during their synthesis render them promising agents for drug-delivery applications in several pharmaceutical formulations. Additionally, dendrimers can be used for reducing the drug toxicity and for the enhancement of the drug efficacy. This review aims to discuss the properties that turn dendrimers into pharmaceutical excipients and their potential applications in the pharmaceutical and biomedical fields.

DFT-based theoretical prediction of intrinsic viscosity of polymer solutions

A four-descriptor quantitative structure-property relationship model was constructed to predict 65 intrinsic viscosities [η] of polymer solutions. Four quantum chemical descriptors, the traceless quadrupole moment θ_(R), the hydrogen bond or electrostatic attraction descriptor Q_H, the partition function Q_BOT(R) and the frontier orbital descriptor E_HOMO, were calculated with density functional theory at the B3LYP/6-31G(d) level and used to develop the model by multivariate linear regression (MLR) analysis. The model possesses coefficients of determination r² of 0.827 for the training set and 0.808 for the test set, and shows better statistical characteristics than the existing MLR models of intrinsic viscosities [η] of polymer-solvent combinations. Moreover, the four descriptors were used to develop a support vector machine model for [η] that possesses a coefficient of determination r² of 0.911 for the whole data set.

Reversible Self-Assembly of Backbone-Thermoresponsive Long Chain Hyperbranched Poly(N-Isopropyl Acrylamide)

In this paper, we mainly described the reversible self-assembly of a backbone-thermoresponsive, long-chain, hyperbranched poly(N-isopropyl acrylamide) (LCHBPNIPAM) in aqueous solution. Here, we revealed a reversible self-assembly behavior of LCHBPNIPAM aqueous solution derived from temperature. By controlling the temperature of LCHBPNIPAM aqueous solution, we tune the morphology of the LCHBPNIPAM self-assemblies. When the solution temperature increased from the room temperature to the lower critical solution temperature of PNIPAM segments, LCHBPNIPAM self-assembled from multi-compartment vesicles into solid micelles. The morphology of LCHBPNIPAM self-assemblies changed from solid micelles to multi-compartment vesicles again when the temperature decreased back to the room temperature. The size presented, at first, an increase, and then a decrease, tendency in the heating-cooling process. The above thermally-triggered self-assembly behavior of LCHBPNIPAM aqueous solution was investigated by dynamic/static light scattering, transmission electron microscopy, atomic force microscopy, fluorescence spectroscopy, ¹H nuclear magnetic resonance in D₂O, and attenuated total reflectance Fourier transform infrared spectroscopy. These results indicated that LCHBPNIPAM aqueous solution presents a reversible self-assembly process. The controlled release behaviors of doxorubicin from the vesicles and micelles formed by LCHBPNIPAM further proved the feasibility of these self-assemblies as the stimulus-responsive drug delivery system.

Probing the molecular design of hyper-branched aryl polyesters towards lubricant applications

We report novel polymeric materials that may be used as viscosity index improvers (VII) for lubricant applications. Our efforts included probing the comb-burst hyper-branched aryl polyester architecture for beneficial viscosity and friction behavior when utilized as an additive in a group I oil. The monomer was designed as to undergo polymerization via polycondensation within the architectural construct (AB2), typical of hyperbranched polymers. The monomer design was comprised of aliphatic arms (12 or 16 methylenes) to provide the necessary lipophilicity to achieve solubility in a non-polar medium. Once polymerized, via catalyst and heat, the surface alcohols were functionalized with fatty acids (lauric and palmitic). Controlling the aliphatic nature of the internal arms and peripheral end-groups provided four unique flexible polymer designs. Changing the reaction time and concentration provided opportunities to investigate the influence of molecular weight and branching density on oil-solubility, viscosity, and friction. Oil-solubility was found to decrease with fewer internal carbons, but the number of internal carbons appears to have little influence on the bulk solution viscosity. At concentrations of 2 wt % in a group I base oil, these polymer additives demonstrated an improved viscosity index and reduced friction coefficient, validating the basic approach.

Hydrodynamic behaviors of amphiphilic dendritic polymers with different degrees of amidation

This work highlights the structure evolution and the response to solvent quality of ADPs.

Synthesis and self-assembly behavior of POSS-embedded hyperbranched polymers

We demonstrate a simple approach to prepare POSS-embedded hyperbranched amphiphiles, presenting morphological transition from micelle to vesicle in aqueous solution.

Single-chain nanoparticles vs. star, hyperbranched and dendrimeric polymers: effect of the nanoscopic architecture on the flow properties of diluted solutions

The flow properties of dilute solutions of linear, star, hyperbranched and dendrimeric polymers have been the subject of numerous studies. However, no systematic analysis has been carried out for the case of single-chain nanoparticles (SCNPs) of different nature, which are unimolecular soft nano-objects consisting of individual polymer chains collapsed to a certain degree by means of intramolecular bonding. On the basis of the fractal nature of SCNPs and experimental data of the hydrodynamic radius, a simple predictive power-law between the intrinsic viscosity and molecular weight is proposed. Furthermore, a comparison is made between the intrinsic viscosities of SCNPs and of low-functionality stars, hyperbranched and dendrimeric polymers of the same chemical nature and molecular weight. As a consequence of their complex nanoscopic architecture, the intrinsic viscosities of SCNPs are systematically smaller than those of linear chains and low-functionality stars. When compared with hyperbranched and dendrimeric polymers, a complex behaviour is found, this being highly dependent on the molecular weight and amount of X-linkers of SCNPs.