Ultrasonic measurements of an epoxy resin near its sol-gel transition

Simultaneous measurements of ultrasound attenuation, phase velocity, thickness, and density spectra of polymeric sheets

The size distribution and mechanical properties of microparticle dispersed in liquid can be characterized by ultrasonic spectroscopy with the aid of acoustic scattering theories. In order to carry out the accurate analysis of the particles, the basic properties, such as the density, viscosity, longitudinal and shear velocities and intrinsic attenuation coefficient of the particle must be known prior to the analysis. Particularly, for soft elastomers or rubbers which exhibit complex mechanical properties with comparable real and imaginary parts, such fundamental information should be provided prior to the particle analysis to minimize the uncertainty of estimation associated with the number of adjustable parameters. In this study, we examined the acoustical properties of poly(methyl methacrylate)(PMMA) and cross-linked poly(dimethyl siloxane) sheets having different cross-linker concentrations by Multiple-Echo Reflection Ultrasonic Spectroscopy which simultaneously enabled us to acquire 4 fundamental properties, the ultrasound attenuation coefficient, phase velocity, density, and thickness (MERUS4 for solid plate). In addition, it was confirmed that the acoustic spectra of PMMA particles dispersed in water were reproduced well with the physical properties determined by MERUS4 using the PMMA plates.

Origin of the anomalous decrease in the apparent density of polymer gels observed by multi-echo reflection ultrasound spectroscopy

Multi-echo reflection ultrasound spectroscopy (MERUS), which enables one to simultaneously evaluate the attenuation coefficient α, the sound velocity v and the density ρ, has been developed for measurements of elastic moduli. In the present study, the technique was further developed to analyze systems undergoing gelation where an unphysical decrease in the apparent density was previously observed after polymerization. The main reason for this problem was that the shrinkage accompanying the gelation led to a small gap between the cell wall and the sample, resulting in the superposition of the reflected signals which were not separable into individual components. By taking into account the multiply reflecting echoes at the interface of the gap, the corrected densities were systematically obtained and compared with the results for the floating test. The present technique opens a new route to simultaneously evaluate the three parameters α, v and ρ and also the sample thickness for solid thin films.

Ultrasonic self-calibrated method applied to monitoring of sol-gel transition

In many industrial processes where online control is necessary such as in the food industry, the real time monitoring of visco-elastic properties is essential to ensure the quantity of production. Acoustic methods have shown that reliable properties could be obtained from measurements of velocity and attenuation. This paper proposes a simple, real time ultrasound method for monitoring linear medium properties (phase velocity and attenuation) that vary in time. The method is based on a pulse echo measurement and is self-calibrated. Results on a silica gel are reported and the importance of taking into account the changes of the mechanical loading on the front face of the transducer will be shown. This is done through a modification of the emission and reception transfer parameters. The simultaneous measurement of the input and output currents and voltages enables these parameters to be calculated during the reaction. The variations of the transfer parameters are in the order of 6% and predominate other effects. The evolution of the ultrasonic longitudinal wave phase velocity and attenuation as a function of time allows the characteristic times of the chemical reaction to be determined. The results are well correlated with the gelation time measured by rheological method at low frequency.

Ultrasonic characterization of a fluid layer using a broadband transducer

A measurement method is proposed for the ultrasonic characterization of a fluid layer, corresponding to the resin transfer molding (RTM) manufacturing process. The ultrasonic velocity and attenuation of the silicone oil are measured in three samples having different viscosities. The measurement method is established on the basis of the attenuation of ultrasonic waves in fluids. A correction of the beam diffraction is implemented to improve measurement precision. A single element transducer with central frequency of 15 MHz is used. The tested fluids simulate the industrial resin used to manufacture composite materials. When injecting this resin, its viscosity increases until it reaches a critical state of polymerization. In this paper we focus on ultrasonic characterization of three fluids representing three intermediate cases of fluid resin during its injection before reaching the polymerization state.

Simultaneous evaluation of ultrasound velocity, attenuation and density of polymer solutions observed by multi-echo ultrasound spectroscopy

Ultrasound spectroscopy is a powerful tool to investigate the viscoelastic properties of materials. The longitudinal elastic moduli M' and M(″), or the adiabatic compressibility κ(S) can be evaluated from ultrasound velocity v and attenuation coefficient α via the relation M'=ρv(2) and M(″)=2ραv(3)/ω, where ρ is the density and ω is the angular frequency. So far, the density was independently measured by other equipments or its variation during the chemical reaction has been ignored in the previous literatures. Here we propose a multiple echo method to simultaneously evaluate α, v, ρ, from a single acquisition, enabling us to monitor the polymerization process of acrylamide, where the three parameters vary independently during the reaction. This allows us to analyze the time evolution of the acoustic parameters for polymeric or gelling systems with the better understanding.

Amorphous freezing in two dimensions: from soft coils to rigid particles

The topic of the gel transition in two dimensions is revisited by considering data on the shear elasticity of Langmuir monolayers of different spherical objects. Amorphous freezing can be associated to structural percolation in a lattice able to resist shear stresses. The shear modulus and its dependence on the packing fraction are found to strongly depend on the details of the interaction potential and largely differ from expectations for entropic networks. This behaviour can be interpreted in terms of more elaborated percolation theories including central forces and bond-bending forces.

Combined Rheological and Ultrasonic Study of Alginate and Pectin Gels near the Sol−Gel Transition

The sol-gel transition of biopolymer mixtures has been investigated by rheological and ultrasonic measurements. A scaling analysis of the data was performed for both types of measurements. A gel time was determined from rheology for the pure pectin samples, and the data could be fitted to a universal scaling form near the transition point. Its critical exponents are in good agreement with the predictions of scalar percolation theory. In addition, the ultrasonic signal of the pectin samples close to the transition was analyzed in terms of a high-frequency scaling approach for the attenuation and the velocity. For the alginate samples and the mixtures, for which the gel point cannot be determined reliably from rheology, the ultrasonic measurements were analyzed using the same scaling form as for the pectin sample, thus providing a method for estimating the gel point, even in the absence of rheological data.

Sol-gel transition in agar-gelatin mixtures studied with transient elastography

Using the shear wave propagation in solids, the transient elastography technique has been developed to assess the elastic properties of soft tissues. Here, a new approach of transient elastography allows assessing the viscoelastic properties of soft tissues. In this paper, the method is used to follow-up the sol-gel transition of an agar-gelatin mixture noninvasively. The shear wave velocity and shear wave attenuation through the mixture were continuously monitored in the audible range of frequencies (from 50 Hz to 200 Hz). The observed changes in velocities and attenuations as a function of frequency confirmed the validity of the Voigt's model to describe the gel at its stable mechanical state. By a simple inverse problem approach, based on the one-dimensional (1-D) Helmholtz equation, the elasticity and the viscosity of such a mixture were recovered as a function of time. The results obtained are in good agreement with the literature and theoretical predictions. Overall, they demonstrate the high sensitivity of the transient elastography measurements to the rheological parameter changes in agar-gelatin mixtures during gelation.

Entropic elasticity of two-dimensional self-avoiding percolation systems

The sol-gel transition is studied on a purely entropic two-dimensional model system consisting of hard spheres (disks) in which a fraction p of neighbors are tethered by inextensible bonds. We use a new method to measure directly the elastic properties of the system. We find that over a broad range of hard sphere diameters a the rigidity threshold is insensitive to a and indistinguishable from the percolation threshold p(c). Close to p(c), the shear modulus behaves as (p-p(c))(f), where the exponent f approximately 1. 3 is independent of a and is similar to the conductivity exponent in random resistor networks.