Characterisation and modelling of the elastic properties of poly(lactic acid) nanofibre scaffolds Edwin Yesid Go ´mez-Pacho ´n • Francisco Manuel Sa ´nchez-Are ´valo • Federico J. Sabina • Alfredo Maciel-Cerda • Rau ´ l Montiel Campos • Nikola Batina • Israel Morales-Reyes • Ricardo Vera-Graziano Received: 15 March 2013 / Accepted: 31 July 2013 / Published online: 20 August 2013 Ó Springer Science+Business Media New York 2013 Abstract The aim of this study is to predict the elastic response of poly(lactic acid) (PLA) electrospun nanofibre scaffolds through mathematical models based on homog- enisation and the differential replacement method (DRM). These models principally seek to determine and analyse the effects of the internal morphology of the nanofibres on the effective Young’s modulus of polymer nanofibre scaffolds. The microstructure of the nanofibres was first characterised by SEM, XRD, DSC, AFM, and TEM techniques. From this characterisation, strong evidence of a hierarchical core–shell structure was found. With the experimental data, it was possible to design and validate better models than those currently used. In addition, the effects of the elec- trospinning parameters, such as take-up velocity and ther- mal treatment, were analysed and correlated with the morphology and the elastic properties of the nanofibres and their scaffolds. To validate the models’ results, we con- ducted a series of uniaxial tensile tests on the PLA nano- fibre scaffolds. Using the data from the nanofibre measurements, the homogenisation approximations and the model based on the DRM predicted an effective Young’s modulus of 667 and 835 MPa, respectively. The predicted data were in excellent agreement with the experimental results (685–880 MPa). These models will be useful in understanding and evaluating the structure–property rela- tionships of oriented nanofibre scaffolds for medical or biological applications. Introduction Tissue engineering is one of the most demanding branches of biomedicine and requires that the materials used be productive and innovative. Scaffolds and porous materials produced by several techniques are commonly used in tissue engineering [1]. A common strategy in tissue engi- neering is the use of biodegradable biomaterials to mimic the functions of native tissues, which may promote cell growth and extracellular matrix generation [2–9] and match the resultant mechanical properties with those of the target tissue. Among the several techniques to produce scaffolds, electrospinning is one of the most useful and versatile methods for controlling the structural parameters of fibrous scaffolds such as the fibre orientation and diameter, texture and scaffold porosity [7–9]. However, our understanding and ability to predict the mechanical prop- erties of electrospun polymer nanofibres are limited. Some efforts to characterise the mechanical behaviour of fibrous scaffolds used in tissue engineering have been reported by Hong et al. They studied the improvement of the mechanical properties of scaffolds composed of E. Y. Go ´mez-Pacho ´n  F. M. Sa ´nchez-Are ´valo  A. Maciel-Cerda  R. Vera-Graziano (&) Instituto de Investigaciones en Materiales, Universidad Nacional Auto ´noma de Me ´xico, 04510 Mexico DF, Mexico e-mail: graziano@unam.mx E. Y. Go ´mez-Pacho ´n e-mail: edwinyesidgom@yahoo.com.mx F. J. Sabina Instituto de Investigaciones en Matema ´ticas Aplicadas y en Sistemas, Universidad Nacional Auto ´noma de Me ´xico, 04510 Mexico DF, Mexico R. M. Campos Departamento de Polı ´meros, Universidad Auto ´noma Metropolitana, Mexico DF, Mexico N. Batina  I. Morales-Reyes Laboratorio de Nanotecnologı ´a e Ingenierı ´a Molecular, Departamento de Quı ´mica, Universidad Auto ´noma Metropolitana, 09340 Mexico DF, Mexico 123 J Mater Sci (2013) 48:8308–8319 DOI 10.1007/s10853-013-7644-7