Alterations in Cage Structure with Addition of Polymer

1. Microstructure of Gels Liquid State Integral Equation Approach Fluid Structure Clusters and Voids Scattering At Small Angles Experimental System Signature of the Gel Rg/R=0.078 Rg/R=0.078 Total Scattering Intensity : S(q)=SD-B(q)+Sc(q) Phase Diagram Gel c= 0.4 Scattering Theory Introduction Colloid-Polymer mixtures are used in a number of industrial and scientific applications to achieve desired material properties. Understanding the effects of microscopic interactions provides tunable paramaters to manipulate the macroscopic properties such as the flow behavior governed by the underlying phase transitions. Suspensions can undergo both equilibrium and non-equilibrium phase transitions depending on the strength and range of these interactions. Strong short-ranged attractions often give rise to gelation whereas weaker longer ranged attractions result in equilibrium fluid-fluid or fluid-crystal transitions. Here we present a comprehensive study of the microstructure of the gel phase of a well characterized colloidal suspension by Small Angle X-ray Scattering as the gel boundary is traversed. The location of the boundary is controlled by carefully tuning the strength and range of interparticle interactions by adding non-adsorbing polymer. cp/cp*= 0.6 Debye-Bueche Analysis: c= 0.4 PRISM Schweizer and Curro (1987) Rg/R=0.078 Voids suppression of intermediate scattering f R /R Expt Colloid: D = 100 ± 5 nm Sterically Stabilized Silica (Hard Spheres) Polymer: Polystyrene (near theta state) in decalin cp/cp*= 0.6 (inter-cluster) Fluid Structure and Thermodynamics (intra-cluster) PRISM site-site density pair correlation function local structural arrest c g Rg/R=0.078 2.8 # of nearest neighbors coherence of local cage The arrows indicate the path taken in X-ray scattering measurements. gss 0.40 0.053 gps 0.40 0.078 0.45 0.053 xc 0.42 0.06 Clusters feff >fbulk 2.4 q* ~ 2p/D gij(r) Sij(q) Ii Cps S(q*) q Css Fumed Silica Gel q D =2R 100 nm xv q* Is Weak Strong gij(r) Sij(q) 2 Cpp gpp 1 1 Gel polymer self-structure factor 1.6 (r-Rij)/Rij I II Gel Boundary wp Aggregated Clusters Gel No added polymer Fourier Transform clusters of size xc ~ 3-5 D 1 0 0.05 0.1 0.15 “polymer  random coil” qRij q* Hair Gel (Cosmetics) p = monomer; s = sphere S(q) ~ (qD)c c ~ -3.5 at high c • Unphysical fractal exponent at high c •Fluctuations insensitive to cp/cp* and Rg/R • Porod-like exponents suggesting compact clusters with fractally rough surfaces? • Departure from Porod-like decay occurs at intermediate length scale qD ~ 1.5-2. q* c /c * p p Fluid-Crystal S(0) = dimensionless osmotic compressibility • Local structure arrested • Intermediate fluctuations suppressed • Enhanced low angle scattering • Insensitivity of gel structure at ALL measurable length scales to cp/cp*, c • Hard core colloid-colloid interaction • p-p interaction depends on solvent quality • Repulsive polymer segment-sphere interaction • Ensemble-averaged inter-particle spacing is “frozen” after gelation • Experiments fall out of agreement with theory due to non-equilibrium transition Ultra small angle x-ray scattering neutron scattering Confocal microscopy Fluid Gel Athermal good uag(r) Fluid-Fluid Ideal Not near spinodal --Why the upturn in S(q) at small q’s ? Toothpaste (Hygiene) Alterations in Cage Structure with Addition of Polymer Comparisons of Equilibrium Structure with PRISM Traversing vertically at  = 0.4 cp/cp* Hard Spheres I. Adding small amounts of polymers to dense suspensions suppress local colloid “cage” coherence II. Adding large amounts of polymers compresses cage (locally densify) Corresponds to Glass Melting No added polymer Lines : PY LINES: PRISM Excellent agreement with theory Summary • Equilibrium • Theory and experimental measurements of S(q) agree. • Non monotonic variation of “cage” coherence with increasing polymer concentration. • Non-Equilibrium • Scattering experiments suggest formation of heterogeneous regions as gel forms • Ensemble-averaged structure is independent of strength and range of attraction after gelation. The UNICAT facility at the Advanced Photon Source (APS) is supported by the Univ of Illinois at Urbana-Champaign, Materials Research Laboratory (U.S. DOE, the State of Illinois-IBHE-HECA, and the NSF), the Oak Ridge National Laboratory (U.S. DOE under contract with UT-Battelle LLC), the National Institute of Standards and Technology (U.S. Department of Commerce) and UOP LLC. The APS is supported by the U.S. DOE, Basic Energy Sciences, Office of Science under contract No. W-31-109-ENG-38. Funding: DOE-BES via UIUC MRL NSF-NSEC (RPI-UIUC-LANL) Microstructure of Dense Colloid Suspensions and Gels S. Ramakrishnan, S.A. Shah, Y.-L. Chen, K.S. Schweizer, and C.F. Zukoski, Department of Chemical and Biomolecular Engineering, University of Illionois at Urbana-Champaign, IL 61801, Jan Ilavsky Department of Chemical Engineering Purdue University, IN 47097, Pete R. Jemian, Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, IL 61801