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Poly(N-isopropylacrylamide) (PNIPAM) is a synthetic polymer that is widely studied for its thermoresponsive character. However, recent works also reported evidence of a low temperature (protein-like) dynamical transition around 225 K in concentrated PNIPAM suspensions, independently of the polymer architecture, i.e., both for linear chains and for microgels. In this work, we investigate water-polymer interactions by extensive differential scanning calorimetry (DSC) measurements of both systems, in order to understand the effect of the different topological structures on the solution behaviour, in particular regarding crystallization and melting processes. In addition, we compare protiated and deuterated microgels, in both water and deuterated water. The DSC results are complemented by dynamic light scattering experiments, which confirm that the selective isotopic substitution differently affects the solution behaviour. Our findings highlight the important role played by the polymer architecture on the solution behaviour: indeed, microgels turn out to be more efficient confining agents, able to avoid water crystallization in a wider concentration range with respect to linear chains. Altogether, the present data will be valuable to interpret future low-temperature investigations of PNIPAM dispersions, particularly by neutron scattering experiments., Comment: 33 pages, 10 figures

Ionic microgel particles are intriguing systems in which the properties of thermo-responsive polymeric colloids are enriched by the presence of charged groups. In order to rationalize their properties and predict the behaviour of microgel suspensions, it is necessary to develop a coarse-graining strategy that starts from the accurate modelling of single particles. Here, we provide a numerical advancement of a recently-introduced model for charged co-polymerized microgels by improving the treatment of ionic groups in the polymer network. We investigate the thermoresponsive properties of the particles, in particular their swelling behaviour and structure, finding that, when charged groups are considered to be hydrophilic at all temperatures, highly charged microgels do not achieve a fully collapsed state, in favorable comparison to experiments. In addition, we explicitly include the solvent in the description and put forward a mapping between the solvophobic potential in the absence of the solvent and the monomer-solvent interactions in its presence, which is found to work very accurately for any charge fraction of the microgel. Our work paves the way for comparing single-particle properties and swelling behaviour of ionic microgels to experiments and to tackle the study of these charged soft particles at a liquid-liquid interface., Comment: 13 pages, 9 figures

Combining elastic incoherent neutron scattering and differential scanning calorimetry, we investigate the occurrence of the volume phase transition (VPT) in very concentrated PNIPAM microgel suspensions, from a polymer weight fraction of 30~wt\% up to dry conditions. Although samples are arrested at the macroscopic scale, atomic degrees of freedom are equilibrated and can be probed in a reproducible way. A clear signature of the VPT is present as a sharp drop of the mean square displacement of PNIPAM hydrogen atoms obtained by neutron scattering. As a function of concentration, the VPT gets smoother as dry conditions are approached whereas the VPT temperature shows a minimum at about 43~wt\%. This behavior is qualitatively confirmed by calorimetry measurements. Molecular dynamics simulations are employed to complement experimental results and gain further insights into the nature of the VPT, confirming that it involves the formation of an attractive gel state between the microgels. Overall, these results provide evidence that the VPT in PNIPAM-based systems can be detected at different time- and length-scales as well as in overcrowded conditions.

Combining elastic incoherent neutron scattering experiments at different resolutions with molecular dynamics simulations, we report the observation of a protein-like dynamical transition in linear chains of Poly(N-isopropylacrylamide). We identify the onset of the transition at a temperature $T_d$ of about 225~K. Thanks to a novel global fit procedure, we find quantitative agreement between measured and calculated polymer mean-squared displacements at all temperatures and time resolutions. Our results confirm the generality of the dynamical transition in macromolecular systems in aqueous environments, independently of the internal polymer topology.

By means of atomistic molecular dynamics simulations we investigate the behaviour of poly(N-isopropylacrylamide), PNIPAM, in water at temperatures below and above the lower critical solution temperature (LCST), including the undercooled regime. The transition between water soluble and insoluble states at the LCST is described as a cooperative process involving an intramolecular coil-to-globule transition preceding the aggregation of chains and the polymer precipitation. In this work we investigate the molecular origin of such cooperativity and the evolution of the hydration pattern in the undercooled polymer solution. The solution behaviour of an atactic 30-mer at high dilution is studied in the temperature interval from 243 to 323 K with a favourable comparison to available experimental data. In the PNIPAM water soluble states we detect a correlation between polymer segmental dynamics and diffusion motion of bound water, occurring with the same activation energy. Simulation results show that below the coil-to-globule transition temperature PNIPAM is surrounded by a network of hydrogen bonded water molecules and that the cooperativity arises from the structuring of water clusters in proximity to hydrophobic groups. Differently, the perturbation of the hydrogen bond pattern involving water and amide groups occurs above the transition temperature. Altogether these findings reveal that even above the LCST PNIPAM remains largely hydrated and that the coil-to-globule transition is related with a significant rearrangement of the solvent in proximity of the surface of the polymer. The comparison between the hydrogen bonding of water in the surrounding of PNIPAM isopropyl groups and in bulk displays a decreased structuring of solvent at the hydrophobic polymer-water interface across the transition temperature, as expected because of the topological extension along the chain of such interface.

Microgels are complex macromolecules. These colloid-sized polymer networks possess internal degrees of freedom and, depending on the polymer(s) they are made of, can acquire a responsiveness to variations of the environment (temperature, pH, salt concentration, etc.). Besides being valuable for many practical applications, microgels are also extremely important to tackle fundamental physics problems. As a result, these last years have seen a rapid development of protocols for the synthesis of microgels, and more and more research has been devoted to the investigation of their bulk properties. However, from a numerical standpoint the picture is more fragmented, as the inherently multi-scale nature of microgels, whose bulk behaviour crucially depends on the microscopic details, cannot be handled at a single level of coarse-graining. Here we present an overview of the methods and models that have been proposed to describe non-ionic microgels at different length-scales, from the atomistic to the single-particle level. We especially focus on monomer-resolved models, as these have the right level of details to capture the most important properties of microgels, responsiveness and softness. We suggest that these microscopic descriptions, if realistic enough, can be employed as starting points to develop the more coarse-grained representations required to investigate the behaviour of bulk suspensions.

Ultrasoft colloids typically do not spontaneously crystallize, but rather vitrify, at high concentrations. Combining in-situ rheo-SANS experiments and numerical simulations we show that shear facilitates crystallization of colloidal star polymers in the vicinity of their glass transition. With increasing shear rate well beyond rheological yielding, a transition is found from an initial bcc-dominated structure to an fcc-dominated one. This crystal-to-crystal transition is not accompanied by intermediate melting but occurs via a sudden reorganization of the crystal structure. Our results provide a new avenue to tailor colloidal crystallization and crystal-to-crystal transition at molecular level by coupling softness and shear.

Using experiments, theory and simulations, we show that the arrested state observed in a colloidal clay at intermediate concentrations is stabilized by the screened Coulomb repulsion (Wigner glass). Dilution experiments allow us to distinguish this high-concentration disconnected state, which melts upon addition of water, from a low-concentration gel state, which does not melt. Theoretical modelling and simulations reproduce the measured Small Angle X-Ray Scattering static structure factors and confirm the long-range electrostatic nature of the arrested structure. These findings are attributed to the different timescales controlling the competing attractive and repulsive interactions., Comment: Accepted for publication in Physical Review Letters

We study by molecular dynamics the interplay between arrest and crystallization in hard spheres. For state points in the plane of volume fraction ($0.54 \leq phi \leq 0.63$) and polydispersity ($0 \leq s \leq 0.085$), we delineate states that spontaneously crystallize from those that do not. For noncrystallizing (or precrystallization) samples we find isodiffusivity lines consistent with an ideal glass transition at $\phi_g \approx 0.585$, independent of $s$. Despite this, for $s<0.05$, crystallization occurs at $\phi > \phi_g$. This happens on time scales for which the system is aging, and a diffusive regime in the mean square displacement is not reached; by those criteria, the system is a glass. Hence, contrary to a widespread assumption in the colloid literature, the occurrence of spontaneous crystallization within a bulk amorphous state does not prove that this state was an ergodic fluid rather than a glass., Comment: 4 pages, 3 figures

Motivated by old experiments on colloidal suspensions, we report molecular dynamics simulations of assemblies of hard spheres, addressing crystallization and glass formation. The simulations cover wide ranges of polydispersity s (standard deviation of the particle size distribution divided by its mean) and particle concentration. No crystallization is observed for s > 0.07. For 0.02 < s < 0.07, we find that increasing the polydispersity at a given concentration slows down crystal nucleation. The main effect here is that polydispersity reduces the supersaturation since it tends to stabilise the fluid but to destabilise the crystal. At a given polydispersity (< 0.07) we find three regimes of nucleation: standard nucleation and growth at concentrations in and slightly above the coexistence region; "spinodal nucleation", where the free energy barrier to nucleation appears to be negligible, at intermediate concentrations; and, at the highest concentrations, a new mechanism, still to be fully understood, which only requires small re-arrangement of the particle positions. The cross-over between the second and third regimes occurs at a concentration, around 58% by volume, where the colloid experiments show a marked change in the nature of the crystals formed and the particle dynamics indicate an "ideal" glass transition.

Recently we have studied, using numerical simulations, a limited valency model, i.e. an attractive square well model with a constraint on the maximum number of bonded neighbors. Studying a large region of temperatures $T$ and packing fractions $\phi$, we have estimated the location of the liquid-gas phase separation spinodal and the loci of dynamic arrest, where the system is trapped in a disordered non-ergodic state. Two distinct arrest lines for the system are present in the system: a {\it (repulsive) glass} line at high packing fraction, and a {\it gel} line at low $\phi$ and $T$. The former is essentially vertical ($\phi$-controlled), while the latter is rather horizontal ($T$-controlled) in the $(\phi-T)$ plane. We here complement the molecular dynamics results with mode coupling theory calculations, using the numerical structure factors as input. We find that the theory predicts a repulsive glass line -- in satisfactory agreement with the simulation results -- and an attractive glass line which appears to be unrelated to the gel line., Comment: 12 pages, 6 figures. To appear in J. Phys. Condens. Matter, special issue: "Topics in Application of Scattering Methods for Investigation of Structure and Dynamics of Soft Condensed Matter", Fiesole, November 2005

We present a numerical study of the statistical properties of the potential energy landscape of a simple model for strong network-forming liquids. The model is a system of spherical particles interacting through a square well potential, with an additional constraint that limits the maximum number of bonds, $N_{\rm max}$, per particle. Extensive simulations have been carried out as a function of temperature, packing fraction, and $N_{\rm max}$. The dynamics of this model are characterized by Arrhenius temperature dependence of the transport coefficients and by nearly exponential relaxation of dynamic correlators, i.e. features defining strong glass-forming liquids. This model has two important features: (i) landscape basins can be associated with bonding patterns; (ii) the configurational volume of the basin can be evaluated in a formally exact way, and numerically with arbitrary precision. These features allow us to evaluate the number of different topologies the bonding pattern can adopt. We find that the number of fully bonded configurations, i.e. configurations in which all particles are bonded to $N_{\rm max}$ neighbors, is extensive, suggesting that the configurational entropy of the low temperature fluid is finite. We also evaluate the energy dependence of the configurational entropy close to the fully bonded state, and show that it follows a logarithmic functional form, differently from the quadratic dependence characterizing fragile liquids. We suggest that the presence of a discrete energy scale, provided by the particle bonds, and the intrinsic degeneracy of fully bonded disordered networks differentiates strong from fragile behavior., Comment: Final version. Journal of Chemical Physics 124, 204509 (2006)

We examine the vitrification and melting of asymmetric star polymers mixtures by combining rheological measurements with mode coupling theory. We identify two types of glassy states, a {\it single} glass, in which the small component is fluid in the glassy matrix of the big one and a {\it double} glass, in which both components are vitrified. Addition of small star polymers leads to melting of {\it both} glasses and the melting curve has a non-monotonic dependence on the star-star size ratio. The phenomenon opens new ways for externally steering the rheological behavior of soft matter systems., Comment: 4 pages, 4 figures, accepted in Phys. Rev. Lett

PEP-PEO block copolymer micelles offer the possibility to investigate phase behaviour and interactions of star polymers (ultra-soft colloids). A star-like architecture is achieved by an extremely asymmetric block ratio (1:20). Micellar functionality f can be smoothly varied by changing solvent composition (interfacial tension). Structure factors obtained by SANS can be quantitatively described in terms of an effective potential developed for star polymers. The experimental phase diagram reproduces to a high level of accuracy the predicted liquid/solid transition. Whereas for intermediate f a bcc phase is observed, for high f the formation of a fcc phase is preempted by glass formation., Comment: 5 pages, 4 figures, PRL in press

We report a numerical study, covering a wide range of packing fraction $\phi$ and temperature $T$, for a system of particles interacting via a square well potential supplemented by an additional constraint on the maximum number $n_{\rm max}$ of bonded interactions. We show that when $n_{\rm max}<6$, the liquid-gas coexistence region shrinks, giving access to regions of low $\phi$ where dynamics can be followed down to low $T$ without an intervening phase separation. We characterize these arrested states at low densities (gel states) in terms of structure and dynamical slowing down, pointing out features which are very different from the standard glassy states observed at high $\phi$ values., Comment: 4 pages, 5 figures, final version, 1 fig. changed

We calculate the statistical properties of the energy landscape of a minimal model for strong network-forming liquids. Dynamics and thermodynamic properties of this model can be computed with arbitrary precision even at low temperatures. A degenerate disordered ground state and logarithmic statistics for the energy distribution are the landscape signatures of strong liquid behavior. Differences from fragile liquid properties are attributed to the presence of a discrete energy scale, provided by the particle bonds, and to the intrinsic degeneracy of topologically disordered networks., Comment: Revised version

We report calculations of the ground state energies and geometries for clusters of different sizes (up to 80 particles), where individual particles interact simultaneously via a short-ranged attractive -modeled with a generalization of the Lennard-Jones potential- and a long-ranged repulsive Yukawa potential. We show that, for specific choices of the parameters of the repulsive potential, the ground state energy per particle has a minimum at a finite cluster size. For these values of the parameters in the thermodynamic limit, at low temperatures and small packing fractions -where clustering is favored and cluster-cluster interactions can be neglected- thermodynamically stable cluster phases can be formed. The analysis of the ground state geometries shows that the spherical shape is marginally stable. In the majority of the studied cases, we find that, above a certain size, ground state clusters preferentially grow almost in one dimension., Comment: LaTeX, 23 pages, 9 eps figures

We perform molecular dynamics simulations of short-range attractive colloid particles modeled by a narrow (3% of the hard sphere diameter) square well potential of unit depth. We compare the dynamics of systems with the same thermodynamics but different bond lifetimes, by adding to the square well potential a thin barrier at the edge of the attractive well. For permanent bonds, the relaxation time $\tau$ diverges as the packing fraction $\phi$ approaches a threshold related to percolation, while for short-lived bonds, the $\phi$-dependence of $\tau$ is more typical of a glassy system. At intermediate bond lifetimes, the $\phi$-dependence of $\tau$ is driven by percolation at low $\phi$, but then crosses over to glassy behavior at higher $\phi$. We also study the wavevector dependence of the percolation dynamics., Comment: Revised; 9 pages, 9 figures

By employing computer simulations for a model binary mixture, we show that a reentrant glass transition upon adding a second component only occurs if the ratio $\alpha$ of the short-time mobilities between the glass-forming component and the additive is sufficiently small. For $\alpha \approx 1$, there is no reentrant glass, even if the size asymmetry between the two components is large, in accordance with two-component mode coupling theory. For $\alpha \ll 1$, on the other hand, the reentrant glass is observed and reproduced only by an effective one-component mode coupling theory., Comment: 4 pages, 3 figures

We study the aging dynamics in a model for dense simple liquids, in which particles interact through a hard-core repulsion complemented by a short-ranged attractive potential, of the kind found in colloidal suspensions. In this system, at large packing fractions, kinetically arrested disordered states can be created both on cooling (attractive glass) and on heating (repulsive glass). The possibility of having two distinct glasses, at the same packing fraction, with two different dynamics offers the unique possibility of comparing -- within the same model -- the differences in aging dynamics. We find that, while the aging dynamics of the repulsive glass is similar to the one observed in atomic and molecular systems, the aging dynamics of the attractive glass shows novel unexpected features., Comment: 8 pages, 11 figures, submited to Journal of Chemical Physics

We evaluate thermodynamic, geometric and dynamic properties of a short-ranged square well binary mixture to provide a coherent picture of this simple, but rich, model for colloidal interactions. In particular, we compare the location, in the temperature-packing fraction plane, of the geometrical percolation locus, the metastable liquid-gas spinodal and the glass transition lines. Such comparison provides evidence that the gel-state can not be related to the attractive glass transition line directly. Indications are given for the possibility of an indirect link between the two, via an arrested phase separation process. We finally discuss the possibility that a spherical short range attraction may not be sufficient to produce an equilibrium cluster phase at low packing fraction and low temperatures., Comment: 14 pages, 4 figures. To appear in published proceedings of Unifying Concepts in Granular Materials and Glasses, Capri 2003

The dynamics of star polymers has been investigated via extensive Molecular- and Brownian Dynamics simulations for a large range of functionality $f$ and packing fraction $\eta$. The calculated isodiffusivity curves display both minima and maxima as a function of $\eta$ and minima as a function of $f$. Simulation results are compared with theoretical predictions based on different approximations for the structure factor. In particular, the ideal glass transition line predicted by mode-coupling theory is shown to exactly track the isodiffusivity curves, offering a theoretical understanding for the observation of disordered arrested states in star polymer solutions., Comment: 4 pages, Revtex, to be published in PRL

Previous theoretical, along with early simulation and experimental, studies have indicated that particles with a short-ranged attraction exhibit a range of new dynamical arrest phenomena. These include very pronounced reentrance in the dynamical arrest curve, a logarithmic singularity in the density correlation functions, and the existence of `attractive' and `repulsive' glasses. Here we carry out extensive molecular dynamics calculations on dense systems interacting via a square-well potential. This is one of the simplest systems with the required properties, and may be regarded as canonical for interpreting the phase diagram, and now also the dynamical arrest. We confirm the theoretical predictions for re-entrance, logarithmic singularity, and give the first direct evidence of the coexistence, independent of theory, of the two coexisting glasses. We now regard the previous predictions of these phenomena as having been established., Comment: 15 pages,15 figures; submitted to Phys. Rev. E

We write equations of motion for density variables that are equivalent to Newtons equations. We then propose a set of trial equations parameterised by two unknown functions to describe the exact equations. These are chosen to best fit the exact Newtonian equations. Following established ideas, we choose to separate these trial functions into a set representing integrable motions of density waves, and a set containing all effects of non-integrability. It transpires that the static structure factor is fixed by this minimum condition to be the solution of the Yvon-Born-Green (YBG) equation. The residual interactions between density waves are explicitly isolated in their Newtonian representation and expanded by choosing the dominant objects in the phase space of the system, that can be represented by a dissipative term with memory and a random noise. This provides a mapping between deterministic and stochastic dynamics. Imposing the Fluctuation-Dissipation Theorem (FDT) allows us to calculate the memory kernel. We write exactly the expression for it, following two different routes, i.e. using explicitly Newtons equations, or instead, their implicit form, that must be projected onto density pairs, as in the development of the well-established Mode Coupling Theory (MCT). We compare these two ways of proceeding, showing the necessity to enforce a new equation of constraint for the two schemes to be consistent. Thus, while in the first `Newtonian' representation a simple gaussian approximation for the random process leads easily to the Mean Spherical Approximation (MSA) for the statics and to MCT for the dynamics of the system, in the second case higher levels of approximation are required to have a fully consistent theory.

Extensive molecular dynamics simulation studies of particles interacting via a short ranged attractive square-well (SW) potential are reported. The calculated loci of constant diffusion coefficient $D$ in the temperature-packing fraction plane show a re-entrant behavior, i.e. an increase of diffusivity on cooling, confirming an important part of the high volume-fraction dynamical-arrest scenario earlier predicted by theory for particles with short ranged potentials. The more efficient localization mechanism induced by the short range bonding provides, on average, additional free volume as compared to the hard-sphere case and results in faster dynamics., Comment: 4 pages, 3 figures

Within the framework of the mode-coupling theory of super-cooled liquids, we investigate new phenomena in colloidal systems on approach to their glass transitions. When the inter-particle potential contains an attractive part, besides the usual repulsive hard core, two intersecting liquid-glass transition lines appear, one of which extends to low densities, while the other one, at high densities, shows a re-entrant behaviour. In the glassy region a new type of transition appears between two different types of glasses. The complex phenomenology can be described in terms of higher order glass transition singularities. The various glass phases are characterised by means of their viscoelastic properties. The glass driven by attractions has been associated to particle gels, and the other glass is the well known repulsive colloidal glass. These correspondences, in associations with the new predictions of glassy behaviour mean that such phenomena may be expected in colloidal systems with, for example, strong depletion or other short-ranged attractive potentials., Comment: 17 pages, 8 figures

We discuss the situation where attractive and repulsive portions of the inter-particle potential both contribute significantly to glass formation. We introduce the square-well potential as prototypical model for this situation, and {\it reject} the Baxter as a useful model for comparison to experiment on glasses, based on our treatment within mode coupling theory. We present explicit results for various well-widths, and show that, for narrow wells, there is a useful analytical formula that would be suitable for experimentalist working in the field of colloidal science. We raise the question as to whether, in a more exact treatment, the sticky sphere limit might have an infinite glass transition temperature, or a high but finite one., Comment: 17 pages, 5 figures

To describe the slow dynamics of a system out of equilibrium, but close to a dynamical arrest, we generalize the ideas of previous work to the case where time-translational invariance is broken. We introduce a model of the dynamics that is reasonably general, and show how all of the unknown parameters of this model may be related to the observables or to averages of the noise. One result is a generalisation of the Fluctuation Dissipation Theorem of type two (FDT2), and the method is thereby freed from this constraint. Significantly, a systematic means of implementing the theory to higher order is outlined. We propose the simplest possible closure of these generalized equations, following the same type of approximations that have been long known for the equilibrium case of Mode Coupling Theory (MCT). Naturally, equilibrium MCT equations are found as a limit of this generalized formalism. %We indicate that, within the same general %framework, it should be possible to make higher level approximations, %leading to more general applicability., Comment: 14 pages, Physica A (in press)

The equations of motion for the density modes of a fluid, derived from Newton's equations, are written as a linear generalized Langevin equation. The constraint imposed by the fluctuation-dissipation theorem is used to derive an exact form for the memory function. The resulting equations, solved under the assumption that the noise, and consequently density fluctuations, of the liquid are gaussian distributed, are equivalent to the random-phase-approximation for the static structure factor and to the well known ideal mode coupling theory (MCT) equations for the dynamics. This finding suggests that MCT is the canonical mean-field theory of the fluid dynamics., Comment: 4 pages, REVTEX

We review the nature of glass transitions and the glasses arising from a square-well potential with a narrow and deep well. Our discussion is based on the Mode Coupling Theory, and the predictions of glasses that we make refer to the `ideal' glasses predicted by that theory. We believe that the square well system well represents colloidal particles with attractive interactions produced by grafted polymers, or depletion interactions. It has been recently shown that two types of glass, an attractive and a repulsive one, are predicted by MCT for this model. The former can form at quite low densities. Most of our attention is directed at the mechanical properties of the glasses predicted by this theory. In particular we calculate the elastic shear modulus at zero frequency and the longitudinal stress modulus in the long wavelength limit. Results for both are presented along the glass-liquid transition curves, and their interesting behaviour is explained in terms of the underlying physics of the system., Comment: 30 pages, 8 figures, Latex, submitted to Phys. Rev. E

The transition from a liquid to a glass in colloidal suspensions of particles interacting through a hard core plus an attractive square-well potential is studied within the mode-coupling-theory framework. When the width of the attractive potential is much shorter than the hard-core diameter, a reentrant behavior of the liquid-glass line, and a glass-glass-transition line are found in the temperature-density plane of the model. For small well-width values, the glass-glass-transition line terminates in a third order bifurcation point, i.e. in a A_3 (cusp) singularity. On increasing the square-well width, the glass-glass line disappears, giving rise to a fourth order A_4 (swallow-tail) singularity at a critical well width. Close to the A_3 and A_4 singularities the decay of the density correlators shows stretching of huge dynamical windows, in particular logarithmic time dependence., Comment: 19 pages, 12 figures, Phys. Rev. E, in print