Exploring non-equilibrium processes and spatio-temporal scaling laws in heated egg yolk using coherent X-rays

The soft-grainy microstructure of cooked egg yolk is the result of a series of out-of-equilibrium processes of its protein-lipid contents; however, it is unclear how egg yolk constituents contribute to these processes to create the desired microstructure. By employing X-ray photon correlation spectroscopy, we investigate the functional contribution of egg yolk constituents: proteins, low-density lipoproteins (LDLs), and yolk-granules to the development of grainy-gel microstructure and microscopic dynamics during cooking. We find that the viscosity of the heated egg yolk is solely determined by the degree of protein gelation, whereas the grainy-gel microstructure is controlled by the extent of LDL aggregation. Overall, protein denaturation-aggregation-gelation and LDL-aggregation follows Arrhenius-type time-temperature superposition (TTS), indicating an identical mechanism with a temperature-dependent reaction rate. However, above 75 °C TTS breaks down and temperature-independent gelation dynamics is observed, demonstrating that the temperature can no longer accelerate certain non-equilibrium processes above a threshold value.

X-ray driven and intrinsic dynamics in protein gels

We use X-ray photon correlation spectroscopy to investigate how structure and dynamics of egg white protein gels are affected by X-ray dose and dose rate. We find that both, changes in structure and beam-induced dynamics, depend on the viscoelastic properties of the gels with soft gels prepared at low temperatures being more sensitive to beam-induced effects. Soft gels can be fluidized by X-ray doses of a few kGy with a crossover from stress relaxation dynamics (Kohlrausch-Williams-Watts exponents [Formula: see text] to 2) to typical dynamical heterogeneous behavior ([Formula: see text]1) while the high temperature egg white gels are radiation-stable up to doses of 15 kGy with [Formula: see text]. For all gel samples we observe a crossover from equilibrium dynamics to beam induced motion upon increasing X-ray fluence and determine the resulting fluence threshold values [Formula: see text]. Surprisingly small threshold values of [Formula: see text] s[Formula: see text] nm[Formula: see text] can drive the dynamics in the soft gels while for stronger gels this threshold is increased to [Formula: see text] s[Formula: see text] nm[Formula: see text]. We explain our observations with the viscoelastic properties of the materials and can connect the threshold dose for structural beam damage with the dynamic properties of beam-induced motion. Our results suggest that soft viscoelastic materials can display pronounced X-ray driven motion even for low X-ray fluences. This induced motion is not detectable by static scattering as it appears at dose values well below the static damage threshold. We show that intrinsic sample dynamics can be separated from X-ray driven motion by measuring the fluence dependence of the dynamical properties.

Effects of temperature and ionic strength on the microscopic structure and dynamics of egg white gels

We investigate the thermal gelation of egg white proteins at different temperatures with varying salt concentrations using x-ray photon correlation spectroscopy in the geometry of ultra-small angle x-ray scattering. Temperature-dependent structural investigation suggests a faster network formation with increasing temperature, and the gel adopts a more compact network, which is inconsistent with the conventional understanding of thermal aggregation. The resulting gel network shows a fractal dimension δ, ranging from 1.5 to 2.2. The values of δ display a non-monotonic behavior with increasing amount of salt. The corresponding dynamics in the q range of 0.002-0.1 nm^-1 is observable after major change of the gel structure. The extracted relaxation time exhibits a two-step power law growth in dynamics as a function of waiting time. In the first regime, the dynamics is associated with structural growth, whereas the second regime is associated with the aging of the gel, which is directly linked with its compactness, as quantified by the fractal dimension. The gel dynamics is characterized by a compressed exponential relaxation with a ballistic-type of motion. The addition of salt gradually makes the early stage dynamics faster. Both gelation kinetics and microscopic dynamics show that the activation energy barrier in the system systematically decreases with increasing salt concentration.

Resolving molecular diffusion and aggregation of antibody proteins with megahertz X-ray free-electron laser pulses

X-ray free-electron lasers (XFELs) with megahertz repetition rate can provide novel insights into structural dynamics of biological macromolecule solutions. However, very high dose rates can lead to beam-induced dynamics and structural changes due to radiation damage. Here, we probe the dynamics of dense antibody protein (Ig-PEG) solutions using megahertz X-ray photon correlation spectroscopy (MHz-XPCS) at the European XFEL. By varying the total dose and dose rate, we identify a regime for measuring the motion of proteins in their first coordination shell, quantify XFEL-induced effects such as driven motion, and map out the extent of agglomeration dynamics. The results indicate that for average dose rates below 1.06 kGy μs^-1 in a time window up to 10 μs, it is possible to capture the protein dynamics before the onset of beam induced aggregation. We refer to this approach as correlation before aggregation and demonstrate that MHz-XPCS bridges an important spatio-temporal gap in measurement techniques for biological samples.

Automated matching of two-time X-ray photon correlation maps from phase-separating proteins with Cahn-Hilliard-type simulations using auto-encoder networks

Machine learning methods are used for an automated classification of experimental two-time X-ray photon correlation maps from an arrested liquid-liquid phase separation of a protein solution. The correlation maps are matched with correlation maps generated with Cahn-Hilliard-type simulations of liquid-liquid phase separations according to two simulation parameters and in the last step interpreted in the framework of the simulation. The matching routine employs an auto-encoder network and a differential evolution based algorithm. The method presented here is a first step towards handling large amounts of dynamic data measured at high-brilliance synchrotron and X-ray free-electron laser sources, facilitating fast comparison with phase field models of phase separation.

Reverse-engineering method for XPCS studies of non-equilibrium dynamics

X-ray photon correlation spectroscopy (XPCS) is a powerful tool in the investigation of dynamics covering a broad time and length scale. It has been widely used to probe dynamics for systems in both equilibrium and non-equilibrium states; in particular, for systems undergoing a phase transition where the structural growth kinetics and the microscopic dynamics are strongly intertwined. The resulting time-dependent dynamic behavior can be described using the two-time correlation function (TTC), which, however, often contains more interesting features than the component along the diagonal, and cannot be easily interpreted via the classical simulation methods. Here, a reverse engineering (RE) approach is proposed based on particle-based heuristic simulations. This approach is applied to an XPCS measurement on a protein solution undergoing a liquid-liquid phase separation. It is demonstrated that the rich features of experimental TTCs can be well connected with the key control parameters including size distribution, concentration, viscosity and mobility of domains. The dynamic information obtained from this RE analysis goes beyond the existing theory. The RE approach established in this work is applicable for other processes such as film growth, coarsening or evolving systems.

Interplay between Kinetics and Dynamics of Liquid-Liquid Phase Separation in a Protein Solution Revealed by Coherent X-ray Spectroscopy

Microscopic dynamics of complex fluids in the early stage of spinodal decomposition (SD) is strongly intertwined with the kinetics of structural evolution, which makes a quantitative characterization challenging. In this work, we use X-ray photon correlation spectroscopy to study the dynamics and kinetics of a protein solution undergoing liquid-liquid phase separation (LLPS). We demonstrate that in the early stage of SD, the kinetics relaxation is up to 40 times slower than the dynamics and thus can be decoupled. The microscopic dynamics can be well described by hyper-diffusive ballistic motions with a relaxation time exponentially growing with time in the early stage followed by a power-law increase with fluctuations. These experimental results are further supported by simulations based on the Cahn-Hilliard equation. The established framework is applicable to other condensed matter and biological systems undergoing phase transitions and may also inspire further theoretical work.

Microscopic Dynamics of Liquid-Liquid Phase Separation and Domain Coarsening in a Protein Solution Revealed by X-Ray Photon Correlation Spectroscopy

While the interplay between liquid-liquid phase separation (LLPS) and glass formation in biological systems is highly relevant for their structure formation and thus function, the exact underlying mechanisms are not well known. The kinetic arrest originates from the slowdown at the molecular level, but how this propagates to the dynamics of microscopic phase domains is not clear. Since with diffusion, viscoelasticity, and hydrodynamics, distinctly different mechanisms are at play, the dynamics needs to be monitored on the relevant time and length scales and compared to theories of phase separation. Using x-ray photon correlation spectroscopy, we determine the LLPS dynamics of a model protein solution upon low temperature quenches and find distinctly different dynamical regimes. We observe that the early stage LLPS is driven by the curvature of the free energy and speeds up upon increasing quench depth. In contrast, the late stage dynamics slows down with increasing quench depth, fingerprinting a nearby glass transition. The dynamics observed shows a ballistic type of motion, implying that viscoelasticity plays an important role during LLPS. We explore possible explanations based on the Cahn-Hilliard theory with nontrivial mobility parameters and find that these can only partially explain our findings.

Kinetics of Network Formation and Heterogeneous Dynamics of an Egg White Gel Revealed by Coherent X-Ray Scattering

The kinetics of heat-induced gelation and the microscopic dynamics of a hen egg white gel are probed using x-ray photon correlation spectroscopy along with ultrasmall-angle x-ray scattering. The kinetics of structural growth reveals a reaction-limited aggregation process with a gel fractal dimension of ≈2 and an average network mesh size of ca. 400 nm. The dynamics probed at these length scales reveals an exponential growth of the characteristic relaxation times followed by an intriguing steady state in combination with a compressed exponential correlation function and a temporal heterogeneity. The degree of heterogeneity increases with decreasing length scale. We discuss our results in the broader context of experiments and models describing attractive colloidal gels.

Interplay between Glass Formation and Liquid-Liquid Phase Separation Revealed by the Scattering Invariant

The interplay of the glass transition with liquid-liquid phase separation (LLPS) is a subject of intense debate. We use the scattering invariant Q to probe how approaching the glass transition affects the shape of LLPS boundaries in the temperature/volume fraction plane. Two protein systems featuring kinetic arrest with a lower and an upper critical solution temperature phase behavior, respectively, are studied varying the quench depth. Using Q we noninvasively identify system-dependent differences for the effect of glass formation on the LLPS boundary. The glassy dense phase appears to enter the coexistence region for the albumin-YCl₃ system, whereas it follows the equilibrium binodal for the γ-globulin-PEG system.

Packing and dynamics of a protein solution approaching the jammed state

The packing of proteins and their collective behavior in crowded media is crucial for the understanding of biological processes. Here we study the structural and dynamical evolution of solutions of the globular protein bovine serum albumin with increasing concentration via drying using small angle X-ray scattering and dynamic light scattering. We probe an evolving correlation peak on the scattering profile, corresponding to the inter-protein distance, ξ, which decreases following a power law of the protein volume fraction, φ. The rate of decrease in ξ becomes faster above a protein concentration of ∼200 mg ml-1 (φ = 0.15). The power law exponent changes from 0.33, which is typical of colloidal or protein solutions, to 0.41. During the entire drying process, we observe the development and the growth of two-step relaxation dynamics with increasing φ as revealed by dynamic light scattering. We find three different regimes of the dependence of ξ as a function of φ. In the dilute regime (φ < 0.22), protein molecules are far apart from each other compared to their size. In this case, the dynamics mainly corresponds to Brownian motion. At an intermediate concentration (0.22 < φ < 0.47), inter-protein distances become comparable to the size of protein molecules, leading to a preferential orientation of the ellipsoidal protein molecules along with a possible deformation. In this regime, the dynamics shows two distinct relaxation times. At a very high concentration (φ > 0.47), the system reaches a jammed state. Subsequently, the secondary relaxation time in this state becomes extremely slow. In this state, the protein molecules have approximately one hydration layer. This study contributes to the understanding of protein molecular packing in crowded environments and the phenomenon of density-driven jamming for soft matter systems.

Engineering interfacial entropic effects to generate giant viscosity changes in nanoparticle embedded polymer thin films

Thin polymer and polymer nanocomposite (PNC) films are being extensively used as advanced functional coating materials in various technological applications. Since it is widely known that various properties of these thin films, especially their thermo-mechanical behavior, can be considerably different from the bulk depending on the thickness as well as interaction with surrounding media, it is imperative to study these properties directly on the films. However, quite often, it becomes difficult to perform these measurements reliably due to a dearth of techniques, especially to measure mechnical or transport properties like the viscosity of thin polymer or PNC films. Here, we demonstrate a new method to study the viscosity of PNC thin films using atomic force microscopy based force-distance spectroscopy. Using this method we investigated viscosity and the glass transition, Tg, of PNC thin films consisting of polymer grafted nanoparticles (PGNPs) embedded in un-entangled homopolymer melt films. The PGNP-polymer interfacial entropic interaction parameter, f, operationally controlled through the ratio of grafted and matrix molecular weight, was systematically tuned while maintaining good dispersion even at very high PGNP loadings, φ. We observed both a significant reduction (low f) and giant enhancement (high f) in the viscosity of the PNC thin films with the effect becoming more prominent with increasing φ. Significantly, none of the established theoretical models for viscosity changes observed earlier in suspensions or polymer nanocomposites can explain the observed viscosity variation. Our results thus not only demonstrate the tunability of the interfacial entropic effect to facilitate a dramatic change in the viscosity of PNC coatings, which could be of great utility in various applications of these materials, but also suggest a new regime of viscosity variation in athermal PNC films indicating the possible need for a new theoretical model.

Unification of lower and upper critical solution temperature phase behavior of globular protein solutions in the presence of multivalent cations

In globular protein systems, upper critical solution temperature (UCST) behavior is common, but lower critical solution temperature (LCST) phase transitions are rare. In addition, the temperature sensitivity of such systems is usually difficult to tune. Here we demonstrate that the charge state of globular proteins in aqueous solutions can alter their temperature-dependent phase behavior. We show a universal way to tune the effective protein interactions and induce both UCST and LCST-type transitions in the system using trivalent salts. We provide a phase diagram identifying LCST and UCST regimes as a function of protein and salt concentrations. We further propose a model based on an entropy-driven cation binding mechanism to explain the experimental observations.

Thermal stability and dynamics of soft nanoparticle membranes: role of entropy, enthalpy and membrane compressibility

Nanoparticle based ultra-thin membranes have been shown to have remarkable mechanical properties while also possessing novel electrical, optical or magnetic properties, which could be controlled by tailoring properties at the level of individual nanoparticles. Since in most cases the ultra-thin membranes are coupled to some substrates, the role of membrane-substrate interactions, apart from nanoparticle-nanoparticle interactions become very crucial in understanding their mechanical and thermal stability, as well as their plethora of applications. However, systematic studies in this direction have been conspicuously absent. Here we report thermal stability and the corresponding microscopic dynamics of polymer supported ultra-thin membranes comprising of self-assembled, ordered grains of polymer grafted nanoparticles having tunable mechanical properties. The initially ordered membranes show distinct pathways for temperature induced disordering depending on membrane flexibility as well as on interfacial entropic and enthalpic interactions with the underlying polymer thin film. We also observe contrasting temperature dependence of microscopic dynamics of these membranes depending on whether the graft polymer-substrate polymer interactions are predominantly entropic or enthalpic in nature. Our results suggest that apart from their varied applications, the soft nanoparticle-polymer hybrid membranes are a playground for rich physics involving subtle entropic and enthalpic effects along with the nanoparticles softness, which eventually determine their thermo-mechanical stability.

Viscosity and fragility of confined polymer nanocomposites: a tale of two interfaces

Viscosity and fragility are key parameters determining the processability and thermo-mechanical stability of glassy polymers and polymer nanocomposites (PNCs). In confined polymers, these parameters are largely dominated by the long relaxation times of the polymers adsorbed at the substrate-polymer interface. On the other hand, for polymer nanocomposites, the interface layer (IL) between the nanoparticles and the surrounding matrix chains often control not only the morphology and dispersion but also various parameters like viscosity and glass transition temperature. Confined PNCs, hence, present a unique opportunity to study the interplay of these two independent interfacial effects. Here, we report the results of X-ray scattering based dynamics measurements of PNC thin films, with a two IL width, unraveling the subtle interplay of these two interfaces on the measured viscosity and fragility. Coupled with coarse-grained molecular dynamics (MD) simulations, our experimental results demonstrate that the viscosity of the PNC films increases with both the IL width and the thickness of the polymer layer adsorbed at the substrate interface. However, while both pristine PS and PNCs with a higher IL width become stronger glasses, as estimated by their fragility, the PNC with a lower IL width shows an increase in fragility with increasing confinement. Our results suggest a novel method to control thermo-mechanical properties and stability of PNC coatings by independently controlling the two interfacial effects in athermal glassy PNCs.

Nanoparticle-polymer interfacial layer properties tune fragility and dynamic heterogeneity of athermal polymer nanocomposite films

Enthalpic interactions at the interface between nanoparticles and matrix polymers are known to influence various properties of the resultant polymer nanocomposites (PNC). For athermal PNCs, consisting of grafted nanoparticles embedded in chemically identical polymers, the role and extent of the interface layer (IL) interactions in determining the properties of the nanocomposites are not very clear. Here, we demonstrate the influence of the interfacial layer dynamics on the fragility and dynamical heterogeneity (DH) of athermal and glassy PNCs. The IL properties are altered by changing the grafted to matrix polymer size ratio, f, which in turn changes the extent of matrix chain penetration into the grafted layer, λ. The fragility of PNCs is found to increase monotonically with increasing entropic compatibility, characterised by increasing λ. Contrary to observations in most polymers and glass formers, we observe an anti-correlation between the dependence on IL dynamics of fragility and DH, quantified by the experimentally estimated Kohlrausch-Watts-Williams parameter and the non-Gaussian parameter obtained from simulations.

Correlation between grafted nanoparticle-matrix polymer interface wettability and slip in polymer nanocomposites

Controlling and understanding the flow properties of polymer nanocomposites (PNC) is very important in realising their potential for various applications. In this study we report molecular dynamics simulation studies of slip between a rotating polymer-grafted nanoparticle and the surrounding free linear matrix chains. By varying the interface wettability between the nanoparticle and matrix chains defined by the parameter f, the ratio of the graft to the matrix chain length, or the graft chain density, Σ, we were able to tune the interface slip, δ, significantly. Both f and Σ alter the interface wettability by changing the matrix chain penetration depth, λ, into the graft chain layer. We observed a large value of δ at smaller f or Σ which reduces with an increasing value of the respective parameters. Since interface slip is also likely to affect other properies of PNCs, like viscosity and the glass transition, we suggest that these parameters could become useful tools to control the flow and mechanical properties of PNCs made with grafted nanoparticles.

Kinetics of dispersion of nanoparticles in thin polymer films at high temperature

We report the first detailed study of the kinetics of dispersion of nanoparticles in thin polymer films using temperature dependent in situ X-ray scattering measurements. We show a comparably enhanced dispersion at higher temperatures for systems which are otherwise phase segregated at room temperature. Detailed analysis of the time dependent X-ray reflectivity and diffuse scattering data allows us to explore the out-of-plane and in-plane mobility of the nanoparticles in the polymer films. While the out-of-plane motion is diffusive with a diffusion coefficient almost two orders of magnitude lower than that expected in bulk polymer, the in-plane one is found to be super-diffusive resulting in significantly larger in-plane displacement at similar time scales. We discuss the origin of the observed highly anisotropic motion of nanoparticles due to their slaved motion with respect to the anisotropic chain orientation and consequent diffusivity anisotropy of matrix chains. We also suggest strategies to utilize these observations to kinetically improve dispersion in otherwise thermodynamically segregated polymer nanocomposite films.