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 $\theta$-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.Comment: 20 pages, 17 figure

Theorem on the Distribution of Short-Time Particle Displacements with Physical Applications

The distribution of the initial short-time displacements of particles is considered for a class of classical systems under rather general conditions on the dynamics and with Gaussian initial velocity distributions, while the positions could have an arbitrary distribution. This class of systems contains canonical equilibrium of a Hamiltonian system as a special case. We prove that for this class of systems the nth order cumulants of the initial short-time displacements behave as the 2n-th power of time for all n>2, rather than exhibiting an nth power scaling. This has direct applications to the initial short-time behavior of the Van Hove self-correlation function, to its non-equilibrium generalizations the Green's functions for mass transport, and to the non-Gaussian parameters used in supercooled liquids and glasses.Comment: A less ambiguous mathematical notation for cumulants was adopted and several passages were reformulated and clarified. 40 pages, 1 figure. Accepted by J. Stat. Phy

Non-Arrhenius Behavior of Secondary Relaxation in Supercooled Liquids

Dielectric relaxation spectroscopy (1 Hz - 20 GHz) has been performed on supercooled glass-formers from the temperature of glass transition (T_g) up to that of melting. Precise measurements particularly in the frequencies of MHz-order have revealed that the temperature dependences of secondary beta-relaxation times deviate from the Arrhenius relation in well above T_g. Consequently, our results indicate that the beta-process merges into the primary alpha-mode around the melting temperature, and not at the dynamical transition point T which is approximately equal to 1.2 T_g.Comment: 4 pages, 4 figures, revtex

Atomic motions in the αβ\alpha\beta-region of glass-forming polymers: Molecular versus Mode Coupling Theory approach

We present fully atomistic Molecular Dynamics simulation results on a main-chain polymer, 1,4-Polybutadiene, in the merging region of the $\alpha$- and $beta$-relaxations. A real space analysis reveals the occurrence of localized motions (``$\beta$-like'') in addition to the diffusive structural relaxation. A molecular approach provides a direct connection between the local conformational changes reflected in the atomic motions and the secondary relaxations in this polymer. Such local processes occur just in the time window where the $\beta$-process of the Mode Coupling Theory is expected. We show that the application of this theory is still possible, and yields an unusually large value of the exponent parameter. This result might originate from the competition between two mechanisms for dynamic arrest: intermolecular packing and intramolecular barriers for local conformational changes (``$\beta$-like'').Comment: 10 pages, 6 figure

Statistical thermodynamics in reversible clustering of gold nanoparticles. A first step towards nanocluster heat engines

A statistical thermodynamics variational criterion is propounded to study thermal hysteresis in reversible clustering of gold (Au) nanoparticles. Experimentally, a transient equilibrium mapping analysis is employed to characterize it thermodynamically, further measurements being performed at the nanostructural and electrochemical levels (UV-Vis-NIR spectra, SLS/SAXS, zeta potential). Theoretically, it is successfully interpreted as a thermodynamic cycle, prompting that nanoclusters has potential to produce useful work from heat and paving the way to nanoclustering heat engines. By taking into account the virial expansion of hysteretic pressure, an entropy measure is deduced for a dilute system with given virial coefficients. This allows us to figure out the role of relevant interparticle potential parameters (i.e. surface potential, nanoparticle size, Debye's length, Hamaker energy) in both isothermal and isochoric variations at the onset of hysteresis. Application to spherical Au nanoparticles in watery salt solution (NaCl) is developed when an ad-hoc (DLVO) pairwise potential governs the second virial coefficient at the nanoscale. In particular, the variational criterion predicts a pressure drop between heating and cooling paths which is likely at the base of some energy redistribution (e.g. ordering/restructuring of electric double layers). We found an integrating factor that is able to numerically predict the existence of a critical value for the initial salt concentration maximizing the hysteretic area, and the effect of nanoparticle size on the cycle extent.A.A. and A.I acknowledge the Grant PID2021-123438NB-I00 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”, as well as financial support of Eusko Jaurlaritza, code: IT-1566-22 and from the IKUR Strategy. A. I. thanks MICINN for a Personal Técnico de Apoyo contract (PTA2017-14359-I). Correspondence of one of the authors (S.A.M.) with Dezső Boda (IASK/UP - Hungary) is kindly acknowledged. This work was supported by grant PID2019-111772RB-I00 funded by MCIN/AEI/ 10.13039/501100011033

Influence of the Environment Fluctuations on Incoherent Neutron Scattering Functions

In extending the conventional dynamic models, we consider a simple model to account for the environment fluctuations of particle atoms in a protein system and derive the elastic incoherent structure factor (EISF) and the incoherent scattering correlation function C(Q,t) for both the jump dynamics between sites with fluctuating site interspacing and for the diffusion inside a fluctuating sphere. We find that the EISF of the system (or the normalized elastic intensity) is equal to that in the absence of fluctuations averaged over the distribution of site interspacing or sphere radius a. The scattering correlation function is $C(Q,t)=\sum_{n} \psi(t)$, where the average is taken over the Q-dependent effective distribution of relaxation rates \lambda_n(a) and \psi(t) is the correlation function of the length a. When \psi(t)=1, the relaxation of C(Q,t) is exponential for the jump dynamics between sites (since \lambda_n(a) is independent of a) while it is nonexponential for diffusion inside a sphere.Comment: 7 pages, 7 eps figure

Advantages of orthogonal folding of single polymer chains to soft nanoparticles

We investigate, by means of computer simulations, the formation of soft nanoparticles by irreversible intramolecular cross-linking of homofunctional polymer precursors in good solvent. Simulations reveal that the early and intermediate stages of the cross-linking process are dominated by bonding at short contour distances. Because of the initial self-avoiding character of the precursor, bonding at long contour distances, which is the efficient mechanism for global compactation, is a rare event that essentially occurs in the late stage of cross-linking. Thus, irreversible cross-linking of precursors with identical molecular weight and linker fraction produces both compact and sparse objects. This is confirmed by a detailed analysis of the size and shape distribution of the fully cross-linked nanoparticles. We also investigate intramolecular cross-linking of heterofunctional polymers with two species of orthogonal linkers, bonding between distinct species being forbidden. It is found that simultaneous cross-linking of both species and sequential cross-linking (activation of one species after full cross-linking of the other) lead to the same structural properties for the resulting nanoparticles. The heterofunctional nanoparticles are on average smaller and more spherical than the homofunctional counterparts, though still a significant fraction of sparse objects is found. The simulation results are compared with results from SEC/MALLS and SAXS experiments in real polymeric nanoparticles. © 2013 American Chemical Society.We acknowledge financial support from Projects No. MAT2012-31088 (Spanish Government) and No. IT654-13 (Basque Government). A.S.-S. expresses thanks for the Ph.D. grant support of the Basque Government (Spain).Peer Reviewe

Design and preparation of single-chain nanocarriers mimicking disordered proteins for combined delivery of dermal bioactive cargos

Inspired by the multifunctionality of vitamin D-binding protein and the multiple transient-binding behavior of some intrinsically disordered proteins (IDPs), a polymeric platform is designed, prepared, and characterized for combined delivery of dermal protective and anticancer bioactive cargos on the basis of artificial single-chain nano-objects mimicking IDPs. For the first time ever, simultaneous delivery of folic acid or vitamin B9, and hinokitiol, a relevant natural bioactive compound that exhibits anticancer activity against human malignant melanoma cells, from these multidirectionally self-assembled unimolecular nanocarriers is illustrated.Financial support from the projects MAT2012–31088 (MINECO) and IT-654–13 (GV) is acknowledged. A.S.-S. thanks the PhD grant support of Basque Government.Peer Reviewe

Static Rouse Modes and Related Quantities: Corrections to Chain Ideality in Polymer Melts

Following the Flory ideality hypothesis intrachain and interchain excluded volume interactions are supposed to compensate each other in dense polymer systems. Multi-chain effects should thus be neglected and polymer conformations may be understood from simple phantom chain models. Here we provide evidence against this phantom chain, mean-field picture. We analyze numerically and theoretically the static correlation function of the Rouse modes. Our numerical results are obtained from computer simulations of two coarse-grained polymer models for which the strength of the monomer repulsion can be varied, from full excluded volume (`hard monomers') to no excluded volume (`phantom chains'). For nonvanishing excluded volume we find the simulated correlation function of the Rouse modes to deviate markedly from the predictions of phantom chain models. This demonstrates that there are nonnegligible correlations along the chains in a melt. These correlations can be taken into account by perturbation theory. Our simulation results are in good agreement with these new theoretical predictions.Comment: 9 pages, 7 figures, accepted for publication in EPJ

Direct observation of molecular cooperativity near the glass transition

We describe direct observations of molecular cooperativity near the glass transition in poly-vinyl-acetate (PVAc), through nanometer-scale probing of dielectric fluctuations. Molecular clusters switched spontaneously between two to four distinct configurations, producing complex random-telegraph-signals (RTS). Analysis of the RTS and their power spectra shows that individual clusters exhibit both transient dynamical heterogeneity and non-exponential kinetics.Comment: 14 pages pdf, need Acrobat Reade