George W. Scherer

Crystallization in pores

This review discusses the thermodynamics of crystallization within porous materials and the factors that influence stress development and cracking. The maximum driving force for crystallization is related to the supersaturation for crystals growing in solution, and to the undercooling for crystals growing from a melt. However, the stresses generated on the pore walls depend on other factors, including the pore size, the energy (γcs) of the interface between the pore wall and the crystal, and (for acicular crystals) the yield stress or buckling strength of the crystal. The fact that growing crystals push particles over large distances indicates that γcs is often large. If γcs were small, crystals would tend to nucleate on pore walls rather than pushing them away, and the crystals would propagate through the pore network without resistance. Even when the crystallization pressure is large, the stress existing in a single pore cannot cause failure because it acts on too small a volume. For fracture to occur, the crystals must propagate through a region of the network large enough that the stress field can interact with the large flaws that control the strength. In concrete, growth on this scale requires that the driving force be sufficient to permit the crystals to pass through pores as small as the breakthrough radius (which is the size of the entry into the percolating network of larger pores that controls the permeability of the body).

Tailored Porous Materials

Tailoring of porous materials involves not only chemical synthetic techniques for tailoring microscopic properties such as pore size, pore shape, pore connectivity, and pore surface reactivity, but also materials processing techniques for tailoring the meso- and the macroscopic properties of bulk materials in the form of fibers, thin films, and monoliths. These issues are addressed in the context of five specific classes of porous materials:  oxide molecular sieves, porous coordination solids, porous carbons, sol−gel-derived oxides, and porous heteropolyanion salts. Reviews of these specific areas are preceded by a presentation of background material and review of current theoretical approaches to adsorption phenomena. A concluding section outlines current research needs and opportunities.

Sol → gel → glass: I. Gelation and gel structure☆

Abstract The mechanisms of gel formation in silicate systems derived from metal alkoxides were reviewed. There is compelling experimental evidence proving, that under many conditions employed in silica gel preparation, the resulting polysilicate species formed prior to gelation is not a dense colloidal particle of anhydrous silica but instead a solvated polymeric chain or cluster. The skeletal gel phase which results during desiccation is, therefore, expected to be less highly crosslinked than the corresponding melted glass, and perhaps to contain additional excess free volume. It is proposed that, during gel densification, the desiccated gel will change to become more highly crosslinked while reducing its surface area and free volume. Thus, it is necessary to consider both the macroscopic physical structure and the local chemical structure of gels in order to explain the gel to glass conversion.

On constrained sintering—I. Constitutive model for a sintering body

Abstract In this series of papers, the constitutive equations used to analyze concurrent shear and densification are critically evaluated. In Part I, it is shown that the sintering materials are not linearly viscoelastic, so Laplace transform techniques cannot be applied. This is not a serious limitation, however, because the relevant deformation of the matrix can be treated as purely viscous flow. Assuming that the strains produced by sintering and applied stresses are linearly additive, a simple constitutive equation is obtained. This will be compared with other constitutive equations from the literature in Part II.

Shrinkage during drying of silica gel

Abstract A model is provided for predicting gel shrinkage during drying by combining the empirical observations that: (1) the bulk modulus of a gel increases with density, ρ, according to K p = K 0 ( ρ ρ y ) m (2.5 ≤ m ≤ 4) ; and (2) the variation in pore radius, r, is approximately proportional to pore volume (contrary to the dependence, r α ρ −1 3 , conventionally assumed). No allowance is made for viscoelastic relaxation, so the model applies only for drying from an inert solvent. The model may be used to guide processing efforts to yield either aerogel-like materials with high porosity or xerogels with high density and small pore size for adsorbents, membranes, etc. The extent of shrinkage is governed by two dimensionless parameters, P and m. The quantity P = As γ cos (θ)mρ y K 0 (where As is specific surface area, γ is surface tension, and θ is the contact angle) represents the relative magnitudes of capillary pressure and gel stiffness, and m describes the variation of stiffness with density. For P values less than 1, the shrinkage upon drying is less than 10%, and is reversible. For shrinkages greater than ⋍ 50%, the density increase is irreversible, and is proportional to P 1/(m - 1). Predicted shrinkage is compared with experimental results for silica gels dried from different surface tension pore fluids (2

On constrained sintering—II. Comparison of constitutive models

Abstract Several authors have proposed constitutive equations to describe bodies that sinter under constraint. We provide a critical examination of these models and show that some of them imply a negative Poissons ratio, in contradiction to experimental evidence.

Theories of relaxation

Abstract The phenomenology of the glass transition is briefly reviewed. Four classes of theories for the transition are discussed: rheological theories that account for the temperature dependence of the viscosity and/or relaxation time τ p ; kinetic theories that predict the form of the relaxation function M p ; relaxation theories that explain both the form of M p and the temperature dependence of τ p ; and phenomenological theories that describe the kinetics of relaxation without reference to a microscopic model.

Sintering inhomogeneous glasses: Application to optical waveguides

Abstract Variations in viscosity or pore size within a glass body cause uneven contraction during sintering. Consequently, stresses develop which alter the local sintering rate and, in some cases, produce bulk flow. This paper illustrates how these stresses can be analyzed by analogy to thermal stress. As a particular example, sintering of optical waveguide preforms made by the OVPO process is examined in detail. The magnitude of the self-stresses, and the conditions required for bulk flow are determined.

Aging and drying of gels

Abstract This review describes the chemical and physical processes occurring during the aging and drying of an inorganic gel. The chemical reactions that lead to gelation are shown to continue long after the solution gels, causing changes in the composition, structure, and properties of the gel. The formation of new crosslinks produces shrinkage (syneresis) and increases the modulus and viscosity of the gel, so that aging reduces the subsequent shrinkage during drying. If the solubility of the solid phase is drying, the small pores of the gel develop high capillary pressures that results in shrinkage. If the exterior surface shrinks much faster than the interior, the differential strain can cause warping and cracking; very slow drying is generally required to prevent such catastrophes. Fracture is most likely at the moment that shrinkage stops and the liquid/vapor meniscus moves into the gel; after that point, the meniscus may remain smooth or may become unstable and ragged. The theory of drying is reviewed and shown to account for the observed behavior. Several strategies are described that minimize the tendency of the gel to crack.

Compression of aerogels

When an aerogel is pressurized in a mercury porosimeter, the network is compressed, but no mercury enters the pores. Therefore, porosimetry cannot be used to measure the pore size distribution in an aerogel, but it does provide a measure of the bulk modulus of the network. For silica aerogels, the network is linearly elastic under small strains, then exhibits yield followed by densification and plastic hardening. In the plastic regime it is found that the bulk modulus has a power-law dependence on density with an exponent of ≈ 3.2. For the same gels, the linear elastic modulus (before compression) also obeys a power law, but the exponent is ⋍ 3.6, as found by several other groups. If a gel is compressed to a pressure, P1, that exceeds the yield stress, then returned to ambient pressure, the plastic deformation is irreversible; if that gel is then compressed to pressure P2 > P1, it behaves elastically up to ⋍ P1, then yields and follows the same power-law curve. Thus the location of the yield point of a previously compressed material indicates the maximum pressure to which the sample had been subjected; in particular, the compression curve can be used to estimate the capillary pressure exerted on a xerogel during drying.