By perturbing about a general monodisperse system, we provide a complete description of twophase equilibria in any system which is slightly polydisperse in some property (e.g. particle size, charge, etc.). We derive a universal law of fractionation which is corroborated by comprehensive experiments on a model colloid-polymer mixture. We furthermore predict that phase separation is an e ective method of reducing polydispersity only for systems with a skewed distribution of the polydisperse property.PACS numbers: 64.10.+h, 82.70.Dd Complex uids contain mesoscopic units that are almost inevitably polydisperse, i.e. colloidal or polymeric particles have some characteristic, such as radius, charge, mass or oblateness, which varies quasi-continuously from one to another. A truly polydisperse system contains in nitely many species with a distribution of properties, and could separate into arbitrarily many coexisting phases. The onset of phase separation is at the`cloud curve', the boundary of coexistence with an in nitesimal amount of a second phase on the`shadow curve'. In contrast to simple systems, a complete description of phase equilibria entails determining not just these limiting curves, but also the di erent compositions (described by a distribution) of arbitrary coexisting phases.Experimentally, phase equilibria have been completely determined for polydisperse polymers 1]. In contrast, most experiments on colloidal phase behavior have ignored polydispersity, despite pragmatic interest in using phase separation to fractionate suspensions 2]; limited data on particulate systems derives only from simulations 3,4]. Many calculations of two-phase equilibria have been attempted for speci c polydisperse systems ( 5] and references therein), especially polymers (which admit mean-eld analysis). The popular but arbitrary method of discretizing the distribution 6], though e cacious, gives little insight. The in nity of coexistence conditions hampers the formulation of truly polydisperse statistical mechanics (discussed in 5,7,8]), especially in non-mean-eld systems, for which exact phase calculations are consequently scarce 9]. The approach of Gualtieri et al. 5] to calculating two-phase coexistence is applicable to a large class of model systems, but gives rise to formidable non-linear equations. They calculate cloud/shadow curves for a polydisperse van der Waals model, but give no general result. We present a simpler treatment, applicable to real systems, and use it to solve the two-phase coexistence problem completely in the limit of small polydispersities. A universal law of fractionation is derived. We show signi cant consistency with comprehensive measurements of phase equilibria in a model polydisperse colloid.Following Gualtieri et al. 5], we divide the total free energy, F tot = F id + F ex into two parts: the free energy of a polydisperse ideal gas of the given species distribution, and the excess due to interactions. The ideal part,
By varying many experimental parameters (temperature, pressure, humidity, contact angle, concentration and volume) we discover that whether evaporating droplets of PEO polymer solution deposit tall solid pillars or flat puddles is controlled by the dimensionless Péclet number, relating flux to diffusion.This article will appear in issue 17 of Soft Matter, a themed issue on Dynamics and Rheology of Fluid Interfaces. AbstractWe report results of a detailed experimental investigation into the drying of sessile droplets of aqueous poly(ethylene oxide) (PEO) polymer solutions under various experimental conditions. Samples are prepared with a range of initial concentrations c 0 and are filtered to remove traces of undissolved PEO clusters. In typical experiments, droplets with initial volumes between 5 L and 50 L are left to evaporate while temperature and relative humidity are monitored. Droplets either form a disk-like solid "puddle" or a tall conical "pillar". The droplet mass is monitored using a microbalance and the droplet profile is recorded regularly using a digital camera. Subsequent processing of the data allows values of droplet volume V, surface area A, base radius R, contact angle θ and height h to be determined throughout drying. From this data we identify four stages during pillar formation: pinned drying; pseudo-dewetting; bootstrap building; solid contraction and propose physical models to explain key aspects of each stage and to predict the transition from each stage to the next. The experimental parameters of relative humidity, temperature, pressure, droplet volume and initial contact angle are all systematically varied and observed to influence the drying process and consequently whether the droplet forms a pillar or a puddle. We combine these parameters into a dimensionless Péclet number Pe, which compares the relative effects of evaporation and diffusion, and show that the drying behaviour is only dependent on c 0 and Pe.
Subjecting charged colloidal particles to a compressional sound wave gives rise to a periodic polarization of the ionic atmosphere surrounding the particles. This periodic polarization causes each particle to act as a vibrating dipole resulting in an alternating voltage, termed the colloid vibration potential (CVP), between any two points in space separated by a phase distance other than an integral multiple of the wavelength and normal to the propagation direction. The present work shows that the CVP is analogous in many respects to the Dorn effect (sedimentation potential) and reflects the same intrinsic phenomena where double-layer relaxation is the dominant process. Both Smoluchowski's theory of the Dorn effect and Enderby's treatment of a charged particle in a sound field are reviewed. Expressions are presented showing the relationship of the CVP to the f potential for dilute colloids. It is also shown how the theory can be extended to particle concentrations as high as 50% by volume using the Levine et al. cell model theory. An apparatus for making electrokinetic measurements using continuous wave ultrasonics is described in detail Data are presented comparing mobilities obtained from CVP measurements and microelectrophoresis. Data are also shown for the dependence of the CVP on particle concentration and compared to predictions based on the proposed modifications using the cell model theory. Also included are data showing the versatility and advantages of acoustical electroki * Author to whom all correspondence should be addressed.
We have studied the kinetics of phase separation in a colloid-polymer mixture. The evolution of initially homogeneous samples as they separate into coexisting colloidal gas, liquid, and crystal phases was investigated by time-lapse video recording. Distinct kinetic regimes were found, the existence and character of which are interpreted in terms of the "free energy landscape" of the system.
Microlitre polymer droplets deposit solid conical structures, via a novel bootstrap drying mechanism, over a range of initial conditions. Accepted for publication in Phys. Chem.Chem.Phys, 2010, DOI: 10.1039 Abstract Sessile droplets of aqueous poly(ethylene oxide) solution, with average molecular weight of 100kDa, are monitored during evporative drying at ambient conditions over a range of initial concentrations c 0 . For all droplets with c 0 ≥ 3%, central conical structures, which can be hollow and nearly 50% taller than the initial droplet, are formed during a growth stage. Although the formation of superficially similar structures has been explained for glass-forming polymers using a skin-buckling model which predicts the droplet to have constant surface area during the growth stage (L.Pauchard and C. Allain, Europhys. Lett., 2003, 62, 897-903), we demonstrate that this model is not applicable here as the surface area is shown to increase during growth for all c 0 . We interpret our experimental data using a proposed drying and deposition process comprising the four stages: pinned drying; receding contact line; "bootstrap" growth, during which the liquid droplet is lifted upon freshly-precipitated solid; and late drying. Additional predictions of our model, including a criterion for predicting whether a conical structure will form, compare favourably with observations. We discuss how the specific chemical and physical properties of PEO, in particular its amphiphilic nature, its tendency to form crystalline spherulites rather than an amorphous glass at high concentrations and its anomalous surface tension values for M W = 100 kDa may be critical to the observed drying process.
In this work, we present the visualization of the internal flows in a drying sessile polymer dispersion drop on hydrophilic and hydrophobic surfaces with Spectral Radar Optical Coherence Tomography (SR-OCT). We have found that surface features such as the initial contact angle and pinning of the contact line, play a crucial role on the flow direction and final shape of the dried drop. Moreover, imaging through selection of vertical slices using optical coherence tomography offers a feasible alternative compared to imaging through selection of narrow horizontal slices using confocal microscopy for turbid, barely transparent fluids.
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