Temperature-induced migration of electro-neutral interacting colloidal particles.

Migration of colloidal particles induced by temperature gradients is commonly referred to as thermodiffusion, thermal diffusion, or the (Ludwig-)Soret effect. The thermophoretic force experienced by a colloidal particle that drives thermodiffusion consists of two distinct contributions: a contribution resulting from internal degrees of freedom of single colloidal particles, and a contribution due to the interactions between the colloids. We present an irreversible thermodynamics based theory for the latter collective contribution to the thermophoretic force. The present theory leads to a novel "thermophoretic interaction force" (for uncharged colloids), which has not been identified in earlier approaches. In addition, an N-particle Smoluchowski equation including temperature gradients is proposed, which complies with the irreversible thermodynamics approach. A comparison with experiments on colloids with a temperature dependent attractive interaction potential over a large concentration and temperature range is presented. The comparison shows that the novel thermophoretic interaction force is essential to describe data on the Soret coefficient and the thermodiffusion coefficient.

Motility-induced inter-particle correlations and dynamics: a microscopic approach for active Brownian particles.

Amongst the theoretical approaches towards the dynamics and phase behaviour of suspensions of active Brownian particles (ABPs), no attempt has been made to specify the motility-induced inter-particle correlations as quantified by the pair-correlation function. Here, we derive expressions for the pair-correlation function for ABPs with very short-ranged direct interactions for small and large swimming velocities and low concentrations. The pair-correlation function is the solution of a differential equation that is obtained from the Fokker-Planck equation for the probability density function of the positions and orientations of the ABPs. For large swimming Peclet numbers, λ, the pair-correlation function is highly asymmetric. The pair-correlation function attains a large value, ∼λ, within a small region of spatial extent, ∼1/λ, near contact of the ABPs when the ABPs approach each other. The pair-correlation function is small within a large region of spatial extent, ∼λ1/3, when the ABPs move apart, with a contact value that is essentially zero. From the explicit expressions for the pair-correlation function, Fick's diffusion equation is generalized to include motility. It is shown that mass transport, in case of large swimming velocities, is dominated by a preferred swimming direction that is induced by concentration gradients. The expression for the pair-correlation function derived in this paper could serve as a starting point to obtain approximate results for high concentrations, which could then be employed in a first-principles analysis of the dynamics and phase behaviour of ABPs at higher concentrations.

Image-guided Radiotherapy to Manage Respiratory Motion: Lung and Liver.

Organ motion as a result of respiratory and cardiac motion poses significant challenges for the accurate delivery of radiotherapy to both the thorax and the upper abdomen. Modern imaging techniques during radiotherapy simulation and delivery now permit better quantification of organ motion, which in turn reduces tumour and organ at risk position uncertainty. These imaging advances, coupled with respiratory correlated radiotherapy delivery techniques, have led to the development of a range of approaches to manage respiratory motion. This review summarises the key strategies of image-guided respiratory motion management with a focus on lung and liver radiotherapy.

Non-local stresses in highly non-uniformly flowing suspensions: The shear-curvature viscosity.

For highly non-uniformly flowing fluids, there are contributions to the stress related to spatial variations of the shear rate, which are commonly referred to as non-local stresses. The standard expression for the shear stress, which states that the shear stress is proportional to the shear rate, is based on a formal expansion of the stress tensor with respect to spatial gradients in the flow velocity up to leading order. Such a leading order expansion is not able to describe fluids with very rapid spatial variations of the shear rate, like in micro-fluidics devices and in shear-banding suspensions. Spatial derivatives of the shear rate then significantly contribute to the stress. Such non-local stresses have so far been introduced on a phenomenological level. In particular, a formal gradient expansion of the stress tensor beyond the above mentioned leading order contribution leads to a phenomenological formulation of non-local stresses in terms of the so-called "shear-curvature viscosity". We derive an expression for the shear-curvature viscosity for dilute suspensions of spherical colloids and propose an effective-medium approach to extend this result to concentrated suspensions. The validity of the effective-medium prediction is confirmed by Brownian dynamics simulations on highly non-uniformly flowing fluids.

Shear-banding in entangled xanthan solutions: tunable transition from sharp to broad shear-band interfaces.

We report on the smooth transition between gradient-banded velocity profiles with a sharp interface and curved velocity profiles, both resulting from strong shear-thinning dispersions of concentrated xanthan (a highly charged poly-saccharide). Pronounced shear-banded flow, where two extended shear-bands are separated by a relatively sharp interface, is observed in a limited range of shear rates, at very low ionic strength and at a high concentration, using heterodyne light scattering to measure spatially resolved velocity profiles. The width of the interface between the coexisting shear-bands broadens to span a sizable fraction of the gap of the shear cell, either by changing the shear rate, by lowering the concentration, or by increasing the ionic strength. The broadening results in a smooth transition to highly curved velocity profiles and is connected to a disappearing flow birefringence. Thus, these experiments show that the classic shear-banding instability can give rise to highly curved velocity profiles, due to the existence of broad interfaces between the bands, with an extent of the order or larger than the cell gap width. This observation may aid to resolve the ongoing dispute concerning shear-banding of highly entangled polymeric systems, suggesting that the curved velocity profiles that have been observed in the past are in fact shear-banded states with an unusually broad interface.

Dielectric spectroscopy of ionic microgel suspensions.

The determination of the net charge and size of microgel particles as a function of their concentration, as well as the degree of association of ions to the microgel backbone, has been pursued in earlier studies mainly by scattering and rheology. These methods suffer from contributions due to inter-particle interactions that interfere with the characterization of single-particle properties. Here we introduce dielectric spectroscopy as an alternative experimental method to characterize microgel systems. The advantage of dielectric spectroscopy over other experimental methods is that the polarization due to mobile charges within a microgel particle is only weakly affected by inter-particle interactions. Apart from electrode polarization effects, experimental spectra on PNIPAM-co-AA [poly(N-isopropylacrylamide-co-acrylic acid)] ionic microgel particles suspended in de-ionized water exhibit three well-separated relaxation modes, which are due to the polarization of the mobile charges within the microgel particles, the diffuse double layer around the particles, and the polymer backbone. Expressions for the full frequency dependence of the electrode-polarization contribution to the measured dielectric response are derived, and a theory is proposed for the polarization resulting from the mobile charges within the microgel. Relaxation of the diffuse double layer is modeled within the realm of a cell model. The net charge and the size of the microgel particles are found to be strongly varying with concentration. A very small value of the diffusion coefficient of ions within the microgel is found, due to a large degree of chemical association of protons to the polymer backbone.

An electric-field induced dynamical state in dispersions of highly charged colloidal rods: comparison of experiment and theory.

Concentrated dispersions of highly charged rod-like colloids (fd-virus particles) in isotropic-nematic coexistence exhibit a dynamical state when subjected to low-frequency electric fields [Soft Matter, 2010, 6, 273]. This dynamical state consists of nematic domains which persistently melt and form on time scales typically of the order of seconds. The origin of the dynamical state has been attributed to a field-induced, cyclic dissociation and association of condensed ions [Soft Matter, 2014, 10, 1987, Soft Matter, 2015, 11, 2893]. The ionic strength increases on dissociation of condensed ions, rendering the nematic domains unstable, while the subsequent decrease of the ionic strength due to association of condensed ions leads to a recurrent stabilization of the nematic state. The role of dissociation/association of condensed ions in the phase/state behaviour of charged colloids in electric fields has not been addressed before. The electric field strength that is necessary to dissociate sufficient condensed ions to render a nematic domain unstable, depends critically on the ambient ionic strength of the dispersion without the external field, as well as the rod-concentration. The aim of this paper is to compare experimental results for the location of transition lines and the dynamics of melting and forming of nematic domains at various ionic strengths and rod-concentrations with the ion-dissociation/association model. Phase/state diagrams in the field-amplitude versus frequency plane at two different ambient ionic strengths and various rod-concentrations are presented, and compared to the theory. The time scale on which melting and forming of the nematic domains occurs diverges on approach of the transition line where the dynamical state appears. The corresponding critical exponents have been measured by means of image time-correlation spectroscopy [Eur. Phys. J. E, 2009, 30, 333], and are compared to the theoretical values predicted by the ion-dissociation/association model.

Glass transition in suspensions of charged rods: structural arrest and texture dynamics.

We report on the observation of a glass transition in suspensions of very long and thin, highly charged colloidal rods (fd-virus particles). Structural particle arrest is found to occur at a low ionic strength due to caging of the charged rods in the potential setup by their neighbors through long-ranged electrostatic interactions. The relaxation time of density fluctuations as probed by dynamic light scattering is found to diverge within a small concentration range. The rod concentration where structural particle arrest occurs is well within the full chiral-nematic state, far beyond the two-phase isotropic-nematic coexistence region. The morphology of the suspensions thus consists of nematic domains with various orientations. We quantify the dynamics of the resulting texture with image-time correlation spectroscopy. Interestingly, the decay times of image correlation functions are found to diverge in a discontinuous fashion at the same concentration of charged rods where structural particle arrest is observed. At the glass-transition concentration, we thus find both structural arrest and freezing of the texture dynamics.

Depletion induced clustering in mixtures of colloidal spheres and fd-virus.

We determined the phase boundary of an ideal rod-sphere mixture consisting of fd-virus, which is an established model system for mono-disperse colloidal rods, and density matched mono-disperse polystyrene beads employing diffuse wave spectroscopy. The low volume fraction of fd needed to induce a phase separation at relatively low ionic strength exemplifies the fact that slender rods are very effective depletion agents. Confocal microscopy showed that stable clusters are formed during phase separation. Relaxation after shear deformation of these clusters showed that the phase separation is gas-liquid-like and that the interfacial tension involved is very low as in colloid-polymer mixtures.

Rotational diffusion of spherical colloids close to a wall.

There is currently no experimental technique available to probe spatially resolved rotational diffusion of nanoparticles in the vicinity of a wall. We present the first experimental study of rotational diffusion of small spherical colloids, using dynamic evanescent wave scattering. A setup is used where the wave vector components parallel and perpendicular to the wall can be varied independently, and an expression is derived for the first cumulant of the intensity correlation function in VH evanescent wave geometry for optically anisotropic spheres. The experimental results are in agreement with theoretical predictions that take particle-wall hydrodynamic interactions into account.

Near-field laser Doppler velocimetry measures near-wall velocities.

A new near-wall velocimetry technique is proposed, based on evanescent wave dynamic light scattering, which allows for the measurement of near-wall velocity profile (characterized by an apparent slip velocity and a shear rate) with a resolution of tens of nanometers. A full theoretical expression of the correlation function is derived for the case of linear flow with negligible Brownian motion. The technique is demonstrated for latex spheres dispersed in water-glycerol mixtures.

Electric-field-induced polarization of the layer of condensed ions on cylindrical colloids.

In concentrated suspensions of charged colloids, interactions between colloids can be induced by an external electric field through the polarization of charge distributions (within the diffusive double layer and the layer of condensed ions) and/or electro-osmotic flow. In case of rod-like colloids, these field-induced inter-colloidal interactions have recently been shown to lead to anomalous orientation perpendicular to the external field, and to phase/state transitions and dynamical states, depending on the field amplitude and frequency of the external field. As a first step towards a (semi-) quantitative understanding of these phenomena, we present a linear-response analysis of the frequency-dependent polarization of the layer of condensed ions on a single, long and thin cylindrical colloid. The in-phase and out-phase response functions for the charge distribution and the electric potential are calculated for arbitrary orientation of the cylindrical colloid. The frequency-dependent degree of alignment, which is proportional to the electric-field-induced birefringence, is calculated as well, and compared to experiments on dilute fd virus suspensions.

Electric-field-induced polarization and interactions of uncharged colloids in salt solutions.

The electric-field-induced charge distribution and potential around a colloidal sphere and rod in salt solutions are analyzed. The resulting field-induced colloid-colloid interactions are calculated for specific orientations. The colloids are assumed to be uncharged (or very weakly charged), such that the deflection of ion fluxes by the cores of the colloids is the dominant polarization mechanism (which is referred to as volume-polarization). Explicit expressions are derived for the frequency-dependent charge distribution and the potential in case of a symmetric electrolyte. It is shown that colloid-colloid interactions due to the induced charge distributions can be much larger than the thermal energy, and are therefore sufficiently strong to give rise to electric-field-induced phase transitions. The present study is a first step towards a quantitative description of field-induced transitions for systems where volume-polarization is the dominant polarization mechanism.

Osmotic shrinkage in star/linear polymer mixtures.

Multiarm star polymers were used as model grafted colloidal particles with long hairs, to study their size variation due to osmotic forces arising from added linear homopolymers of smaller size. This is the origin of the depletion phenomenon that has been exploited in the past as a means to melt soft colloidal glasses by adding linear chains and analyzed using dynamic light scattering experiments and an effective interactions analysis yielding the depletion potential. Shrinkage is a generic phenomenon for hairy particles, which affects macroscopic properties and state transitions at high concentrations. In this work we present a small-angle neutron scattering study of star/linear polymer mixtures with different size ratios (varying the linear polymer molar mass) and confirm the depletion picture, i.e., osmotic star shrinkage. Moreover, we find that as the linear/star polymer size ratio increases for the same effective linear volume fraction (c/c* with c* the overlapping concentration), the star shrinkage is reduced whereas the onset of shrinkage appears to take place at higher linear polymer volume fractions. A theoretical description of the force balance on a star polymer in solution, accounting for the classic Flory contributions, i.e. elastic and excluded volume, as well as the osmotic force due to the linear chains, accurately predicts the experimental findings of reduced star size as a function of linear polymer concentration. This is done in a parameter-free fashion, in which the size of the cavity created by the star, and from which the chains are excluded, is related to the radius of the former from first principles.

The intensity correlation function in evanescent wave scattering.

As a first step toward the interpretation of dynamic light scattering with evanescent illumination from suspensions of interacting spheres, in order to probe their near wall dynamics, we develop a theory for the initial slope of the intensity autocorrelation function. An expression for the first cumulant is derived that is valid for arbitrary concentrations, which generalizes a well-known expression for the short-time, wave-vector dependent collective diffusion coefficient in bulk to the case where a wall is present. Explicit expressions and numerical results for the various contributions to the initial slope are obtained within a leading order virial expansion. The dependence of the initial slope on the components of the wave vector parallel and perpendicular to the wall, as well as the dependence on the evanescent-light penetration depth are discussed. For the hydrodynamic interactions between colloids and between the wall, which are essential for a correct description of the near-interface dynamics, we include both far-field and lubrication contributions. Lubrication contributions are essential to capture the dynamics as probed in experiments with small penetration depths. Simulations have been performed to verify the theory and to estimate the extent of the concentration range where the virial expansion is valid. The computer algorithm developed for this purpose will also be of future importance for the interpretation of experiments and to develop an understanding of near-interface dynamics, at high colloid concentrations.

Rheology and structural arrest of casein suspensions.

The rheology of milk powder suspensions is investigated up to very high concentrations, where structural arrest occurs. The main component of the milk powder investigated is casein, so that the suspensions can be regarded as casein suspensions. Four concentration regimes are identified. For effective casein volume fractions less than 0.54 the concentration dependence of the zero-shear viscosity is similar to that of hard-sphere suspensions. However, due to the elastic deformation of the caseins, the viscosity does not diverge at the hard sphere glass transition. In the volume-fraction range of 0.55-0.61 the viscosity exhibits a surprisingly weak dependence on concentration. The shape of the curve of the shear viscosity versus concentration deviates from hard sphere behavior in an unusual way, due to the observation of a region of almost constant viscosity. This concentration regime is followed by a regime where the viscosity steeply increases, eventually diverging at an effective volume fraction of 0.69. Frequency dependent rheology and diffusing wave spectroscopy measurements indicate that the suspensions are jammed for volume fractions above 0.69. Finally we found the concentration dependence of the relative zero-shear viscosity of casein suspensions to be very similar with the one of the micro-gels at volume fractions below 0.50 and above 0.55, which are know to shrink above a certain volume fraction, due to osmotic stress.

Criticality in a non-equilibrium, driven system: charged colloidal rods (fd-viruses) in electric fields.

Experiments on suspensions of charged colloidal rods (fd-virus particles) in external electric fields are performed, which show that a non-equilibrium critical point can be identified. Several transition lines of field-induced phases and states meet at this point and it is shown that there is a length- and time-scale which diverge at the non-equilibrium critical point. The off-critical and critical behavior is characterized, with both power law and logarithmic divergencies. These experiments show that analogous features of the classical, critical divergence of correlation lengths and relaxation times in equilibrium systems are also exhibited by driven systems that are far out of equilibrium, related to phases/states that do not exist in the absence of the external field.

Attractive colloidal rods in shear flow.

The effect of shear flow on the isotropic-nematic phase transition of attractive colloidal rods is investigated by a combination of simulations and experiments. The isotropic phase aligns with the flow, while the nematic phase undergoes a collective rotational motion which frustrates the merging of the coexisting regions. The location of binodals, spinodals, and the tumbling-to-aligning transition line in the shear-rate versus concentration plane are investigated. The phase diagrams in the shear-concentration plane for the various strengths of attractions can be mapped onto a master curve by appropriate scaling.

Single-particle thermal diffusion of charged colloids: double-layer theory in a temperature gradient.

The double-layer contribution to the single-particle thermal diffusion coefficient of charged, spherical colloids with arbitrary double-layer thickness is calculated and compared to experiments. The calculation is based on an extension of the Debye-Hückel theory for the double-layer structure that includes a small temperature gradient. There are three forces that constitute the total thermophoretic force on a charged colloidal sphere due to the presence of its double layer: i) the force F W that results from the temperature dependence of the internal electrostatic energy W of the double layer, ii) the electric force Fel with which the temperature-induced non-spherically symmetric double-layer potential acts on the surface charges of the colloidal sphere and iii) the solvent-friction force Fsol on the surface of the colloidal sphere due to the solvent flow that is induced in the double layer because of its asymmetry. The force F W will be shown to reproduce predictions based on irreversible-thermodynamics considerations. The other two forces Fel and Fsol depend on the details of the temperature-gradient-induced asymmetry of the double-layer structure which cannot be included in an irreversible-thermodynamics treatment. Explicit expressions for the thermal diffusion coefficient are derived for arbitrary double-layer thickness, which complement the irreversible-thermodynamics result through the inclusion of the thermophoretic velocity resulting from the electric- and solvent-friction force.