Swelling Behavior of Single-Chain Polymer Nanoparticles: Theory and Simulation

Structure of Single-Chain Nanoparticles under Crowding Conditions: A Random Phase Approximation Approach

The conformation of poly(methyl methacrylate) (PMMA)-based single-chain nanoparticles (SCNPs) and their corresponding linear precursors in the presence of deuterated linear PMMA in deuterated dimethylformamide (DMF) solutions has been studied by small-angle neutron scattering (SANS). The SANS profiles were analyzed in terms of a three-component random phase approximation (RPA) model. The RPA approach described well the scattering profiles in dilute and crowded solutions. Considering all the contributions of the RPA leads to an accurate estimation of the single chain form factor parameters and the Flory-Huggins interaction parameter between PMMA and DMF. The value of the latter in the dilute regime indicates that the precursors and the SCNPs are in good solvent conditions, while in crowding conditions, the polymer becomes less soluble.

Neat Protein Single-Chain Nanoparticles from Partially Denatured BSA

The main challenge for the preparation of protein single-chain nanoparticles (SCNPs) is the natural complexity of these macromolecules. Herein, we report the suitable conditions to produce "neat" bovine serum albumin (BSA) single-chain nanoparticles (SCNPs) from partially denatured BSA, which involves denaturation in urea and intramolecular cross-linking below the overlap concentration. We use two disuccinimide ester linkers containing three and six methylene spacer groups: disuccinimidyl glutarate (DSG) and disuccinimidyl suberate (DSS), respectively. Remarkably, the degree of internal cross-linking can be followed simply and efficiently via ¹H NMR spectroscopy. The associated structural changes-as probed by small-angle neutron scattering (SANS)-reveal that the denatured protein has a random-like coil conformation, which progressively shrinks with the addition of DSG or DSS, thus allowing for size control of the BSA-SCNPs with radii of gyration down to 5.4 nm. The longer cross-linker exhibits slightly more efficiency in chain compaction with a somewhat stronger size reduction but similar reactivity at a given cross-linker concentration. This reliable method is applicable to a wide range of compact proteins since most proteins have appropriate reactive amino acids and denature in urea. Critically, this work paves the way to the synthesis of "neat", biodegradable protein SCNPs for a range of applications including nanomedicine.

Validity of Effective Potentials in Crowded Solutions of Linear and Ring Polymers with Reversible Bonds

We perform simulations to compute the effective potential between the centers-of-mass of two polymers with reversible bonds. We investigate the influence of the topology on the potential by employing linear and ring backbones for the precursor (unbonded) polymer, finding that it leads to qualitatively different effective potentials. In the linear and ring cases the potentials can be described by Gaussians and generalized exponentials, respectively. The interactions are more repulsive for the ring topology, in analogy with known results in the absence of bonding. We also investigate the effect of the specific sequence of the reactive groups along the backbone (periodic or with different degrees of randomness), establishing that it has a significant impact on the effective potentials. When the reactive sites of both polymers are chemically orthogonal so that only intramolecular bonds are possible, the interactions become more repulsive the closer to periodic the sequence is. The opposite effect is found if both polymers have the same types of reactive sites and intermolecular bonds can be formed. We test the validity of the effective potentials in solution, in a broad range of concentrations from high dilution to far above the overlap concentration. For this purpose, we compare simulations of the effective fluid and test particle route calculations with simulations of the real all-monomer system. Very good agreement is found for the reversible linear polymers, indicating that unlike in their nonbonding counterparts many-body effects are minor even far above the overlap concentration. The agreement for the reversible rings is less satisfactory, and at high concentration the real system does not show the clustering behavior predicted by the effective potential. Results similar to the former ones are found for the partial self-correlations in ring/linear mixtures. Finally, we investigate the possibility of creating, at high concentrations, a gel of two interpenetrated reversible networks. For this purpose we simulate a 50/50 two-component mixture of reversible polymers with orthogonal chemistry for the reactive sites, so that intermolecular bonds are only formed between polymers of the same component. As predicted by both the theoretical phase diagram and the simulations of the effective fluid, the two networks in the all-monomer mixture do not interpenetrate, and phase separation (demixing) is observed instead.

Characterization of Monte Carlo Dynamic/Kinetic Properties of Local Structure in Bond Fluctuation Model of Polymer System

We report the results of the characterization of local Monte Carlo (MC) dynamics of an equilibrium bond fluctuation model polymer matrix (BFM), in time interval typical for MC simulations of non-linear optical phenomena in host-guest systems. The study contributes to the physical picture of the dynamical aspects of quasi-binary mosaic states characterized previously in the static regime. The polymer dynamics was studied at three temperatures (below, above and close to the glass transition), using time-dependent generalization of the static parameters which characterize local free volume and local mobility of the matrix. Those parameters play the central role in the kinetic MC model of host-guest systems. The analysis was done in terms of the probability distributions of instantaneous and time-averaged local parameters. The main result is the characterization of time scales characteristic of various local structural processes. Slowing down effects close to the glass transition are clearly marked. The approach yields an elegant geometric criterion for the glass transition temperature. A simplified quantitative physical picture of the dynamics of guest molecules dispersed in BFM matrix at low temperatures offers a starting point for stochastic modeling of host-guest systems.

Modeling of Nonlinear Optical Phenomena in Host-Guest Systems Using Bond Fluctuation Monte Carlo Model: A Review

We review the results of Monte Carlo studies of chosen nonlinear optical effects in host-guest systems, using methods based on the bond-fluctuation model (BFM) for a polymer matrix. In particular, we simulate the inscription of various types of diffraction gratings in degenerate two wave mixing (DTWM) experiments (surface relief gratings (SRG), gratings in polymers doped with azo-dye molecules and gratings in biopolymers), poling effects (electric field poling of dipolar molecules and all-optical poling) and photomechanical effect. All these processes are characterized in terms of parameters measured in experiments, such as diffraction efficiency, nonlinear susceptibilities, density profiles or loading parameters. Local free volume in the BFM matrix, characterized by probabilistic distributions and correlation functions, displays a complex mosaic-like structure of scale-free clusters, which are thought to be responsible for heterogeneous dynamics of nonlinear optical processes. The photoinduced dynamics of single azopolymer chains, studied in two and three dimensions, displays complex sub-diffusive, diffusive and super-diffusive dynamical regimes. A directly related mathematical model of SRG inscription, based on the continuous time random walk (CTRW) formalism, is formulated and studied. Theoretical part of the review is devoted to the justification of the a priori assumptions made in the BFM modeling of photoinduced motion of the azo-polymer chains.

Crowded solutions of single-chain nanoparticles under shear flow

Single-chain nanoparticles (SCNPs) are ultrasoft objects obtained through purely intramolecular cross-linking of single polymer chains. By means of computer simulations with implemented hydrodynamic interactions, we investigate for the first time the effect of the shear flow on the structural and dynamic properties of SCNPs in semidilute and concentrated solutions. We characterize the dependence of several conformational and dynamic observables on the shear rate and the concentration, obtaining a set of power-law scaling laws. The concentration has a very different effect on the shear rate dependence of the former observables in SCNPs than in simple linear chains. Whereas for the latter the scaling behaviour is marginally dependent on the concentration, two clearly different scaling regimes are found for the SCNPs below and above the overlap concentration. At fixed shear rate SCNPs and linear chains also respond very differently to crowding. Whereas, at moderate and high Weissenberg numbers the linear chains swell, the SCNPs exhibit a complex non-monotonic behaviour. We suggest that these findings are inherently related to the topological interactions preventing concatenation of the SCNPs, which lead to less interpenetration than for linear chains, and to the limitation to stretching imposed by the permanent cross-links in the SCNPs, which itself limits the ways to spatially arrange in the shear flow.

Advances in the Multi-Orthogonal Folding of Single Polymer Chains into Single-Chain Nanoparticles

The folding of certain proteins (e.g., enzymes) into perfectly defined 3D conformations via multi-orthogonal interactions is critical to their function. Concerning synthetic polymers chains, the "folding" of individual polymer chains at high dilution via intra-chain interactions leads to so-called single-chain nanoparticles (SCNPs). This review article describes the advances carried out in recent years in the folding of single polymer chains into discrete SCNPs via multi-orthogonal interactions using different reactive chemical species where intra-chain bonding only occurs between groups of the same species. First, we summarize results from computer simulations of multi-orthogonally folded SCNPs. Next, we comprehensively review multi-orthogonally folded SCNPs synthesized via either non-covalent bonds or covalent interactions. Finally, we conclude by summarizing recent research about multi-orthogonally folded SCNPs prepared through both reversible (dynamic) and permanent bonds.

Mediating covalent crosslinking of single-chain nanoparticles through solvophobicity in organic solvents

The photoinduced intrachain crosslinking of coumarin-containing copolymers in various organic solvents was mediated through the solvophobic effect, providing control over the reaction rate and the compaction of the final single-chain nanoparticles.

An in-depth analysis approach enabling precision single chain nanoparticle design

The synthesis of single chain nanoparticles (SCNPs) is a vibrant field in macromolecular science. However, to achieve an in-depth understanding of the nature of intramolecular polymer folding, a step-change in the methodologies for SCNP analysis is required.

PET-RAFT and SAXS: High Throughput Tools to Study Compactness and Flexibility of Single-Chain Polymer Nanoparticles

From protein science, it is well understood that ordered folding and 3D structure mainly arises from balanced and noncovalent polar and nonpolar interactions, such as hydrogen bonding. Similarly, it is understood that single-chain polymer nanoparticles (SCNPs) will also compact and become more rigid with greater hydrophobicity and intrachain hydrogen bonding. Here, we couple high throughput photoinduced electron/energy transfer reversible addition-fragmentation chain-transfer (PET-RAFT) polymerization with high throughput small-angle X-ray scattering (SAXS) to characterize a large combinatorial library (>450) of several homopolymers, random heteropolymers, block copolymers, PEG-conjugated polymers, and other polymer-functionalized polymers. Coupling these two high throughput tools enables us to study the major influence(s) for compactness and flexibility in higher breadth than ever before possible. Not surprisingly, we found that many were either highly disordered in solution, in the case of a highly hydrophilic polymer, or insoluble if too hydrophobic. Remarkably, we also found a small group (9/457) of PEG-functionalized random heteropolymers and block copolymers that exhibited compactness and flexibility similar to that of bovine serum albumin (BSA) by dynamic light scattering (DLS), NMR, and SAXS. In general, we found that describing a rough association between compactness and flexibility parameters (R g /R h and Porod Exponent, respectively) with logP, a quantity that describes hydrophobicity, helps to demonstrate and predict material parameters that lead to SCNPs with greater compactness, rigidity, and stability. Future implementation of this combinatorial and high throughput approach for characterizing SCNPs will allow for the creation of detailed design parameters for well-defined macromolecular chemistry.

Tendomers - force sensitive bis-rotaxanes with jump-like deformation behavior

We consider tendomers, which are formed by pairs of rotaxane molecules where each one consists of a linear chain with N Kuhn segments that are threaded through m + 1 small rings. These rings can slide freely along the chains but cannot pass through each other or detach from the chain. By crosslinking the first slide rings of the two rotaxanes a slip-link between the two polymer backbones is formed. The remaining m slide rings form a one-dimensional real gas confined between the slip-link and the other chain end. When pulling the two ends of the chains which are next to the slip-link, an applied external force causes a compression of the slide rings. We consider the exact partition function of this model taking into account the repulsion between the slide rings and the finite extensibility of the polymer chains which is compared with Monte-Carlo simulation data for the tendomer under external force. To understand the underlying physics of the tendomer, we discuss also a simplified thermodynamic approach by taking into account the interplay between chain deformation and compression of the gas of slide rings. We show that tendomers exhibit a jump like mechanical response at a critical pulling force ∝ (m/N)1/2, where the compression of the gas of slide rings sets is. While the tendomer deforms at low forces similar to a short chain of about 2(N - m)/(m + 2) segments, it displays a jump-like decrease in elasticity beyond the critical force and deforms then like a chain of about 2(N - m) segments, before the finite extensibility of the chains sets in. This results in a strong peak of the mechanical susceptibility of the tendomer as a function of the applied force. Thus, tendomers are molecular-elastic elements with a jump-like strain-softening behavior. Our results are generalized to asymmetric tendomers that differ in the number of slide rings per rotaxane, which allows to design multi-step force extension curves with defined critical forces. Finally, we discuss some aspects of gels formed by tendomers, which are promising candidates for tailor-made stress sensitive elastomers.

Strengths and limitations of size exclusion chromatography for investigating single chain folding – current status and future perspectives

Synthetic approaches for Single-Chain Nanoparticles (SCNPs) developed rapidly during the last decade, opening a multitude of avenues for the design of functional macromolecular chains able to collapse into defined nanoparticles. However, the analytical evaluation of the SCNP formation process still requires critical improvements.

Local Domain Size in Single-Chain Polymer Nanoparticles

Single-chain polymer nanoparticles (SCNPs) obtained through chain collapse via intramolecular cross-linking are attracting significant interest for nanomedicine and biomimetic catalysis applications, among other fields. This interest arises from the possibility to bind active species (e.g., drugs and catalysts)-either temporally or permanently-to the SCNP local pockets formed upon chain collapse. However, direct quantification of the size and number of such local domains in solution-even if highly desirable-is currently highly demanding from an experimental point of view because of the small size involved (<5 nm). On the basis of a scaling analysis, we establish herein a connection between the global compaction degree (R/R 0) and the size (ξ) and number (n) of the "collapsed domains" generated upon SCNP formation at high dilution from a linear semiflexible precursor polymer. Results from molecular dynamics simulations and experimental data are used to validate this scaling analysis and to estimate the size and number of local domains in polystyrene SCNPs synthesized through a "click" chemistry procedure, as a representative system, as well as for relevant catalytic SCNPs containing Cu, Pt, and Ni atoms. Remarkably, the present work is a first step toward tuning the local domain size of the next generation of SCNPs for nanomedicine and bioinspired catalysis applications.

The Effect of Intramolecular Cross-Linking on Polymer Interactions in Solution

The conformation of a polymer in a solvent is typically defined by the solvent quality, which is a consequence of the solvent and macromolecule's chemistry. Yet, additional factors can affect the polymer conformation, such as non-covalent interactions to surfaces or other macromolecules, affecting the amount of polymer-solvent interactions. Herein, chemically folded polymers with protein-like architectures are studied and compared to their unfolded linear precursor in good solvents using rheology measurements. The current research reveals that permanent folding by intramolecular chemical cross-linking limits the chain mobility and therefore causes a reduction in polymer-solvent interactions, making a good solvent become theta. This change not only affects the "solvent quality" but also leads to a change in particle-particle interactions as a function of concentration. These findings provide crucial insight into the effects of intramolecular cross-links on macromolecule solubility and self-assembly, which are critical for mimicking structurally similar biological materials.

Effect of chain stiffness on the structure of single-chain polymer nanoparticles

Polymeric single-chain nanoparticles (SCNPs) are soft nano-objects synthesized by purely intramolecular cross-linking of single polymer chains. By means of computer simulations, we investigate the conformational properties of SCNPs as a function of the bending stiffness of their linear polymer precursors. We investigate a broad range of characteristic ratios from the fully flexible case to those typical of bulky synthetic polymers. Increasing stiffness hinders bonding of groups separated by short contour distances and increases looping over longer distances, leading to more compact nanoparticles with a structure of highly interconnected loops. This feature is reflected in a crossover in the scaling behaviour of several structural observables. The scaling exponents change from those characteristic for Gaussian chains or rings in θ-solvents in the fully flexible limit, to values resembling fractal or 'crumpled' globular behaviour for very stiff SCNPs. We characterize domains in the SCNPs. These are weakly deformable regions that can be seen as disordered analogues of domains in disordered proteins. Increasing stiffness leads to bigger and less deformable domains. Surprisingly, the scaling behaviour of the domains is in all cases similar to that of Gaussian chains or rings, irrespective of the stiffness and degree of cross-linking. It is the spatial arrangement of the domains which determines the global structure of the SCNP (sparse Gaussian-like object or crumpled globule). Since intramolecular stiffness can be varied through the specific chemistry of the precursor or by introducing bulky side groups in its backbone, our results propose a new strategy to tune the global structure of SCNPs.