Modeling Diameter Distributions of Poly (N-isopropylacrylamide-co-methacrylic Acid) Nanoparticles Quang Cao, Peng Tian, Qinglin Wu School of Renewable Natural Resources, Louisiana State University Ag Center, Baton Rouge, Louisiana 70803 Received 19 February 2008; accepted 27 August 2008 DOI 10.1002/app.29274 Published online 25 November 2008 in Wiley InterScience (www.interscience.wiley.com). ABSTRACT: The Weibull distribution was successfully used to describe the diameter distribution of poly(N-iso- propylacrylamide-co-methacrylic Acid (PNIPAAm-MAA) nanoparticles, whereas the lognormal was deemed not adequate for that purpose. The method of moments was used to predict parameters of the Weibull distribution. In this approach, the Weibull parameters were recovered from the diameter mean and variance, both of which were predicted from temperature. The distributions predicted from various temperatures for both MAA/NIPAAm ratios of 0.05 and 0.10 showed trends similar to those displayed in the observed data. V V C 2008 Wiley Periodicals, Inc. J Appl Polym Sci 111: 2584–2589, 2009 Key words: PNIPAAm-MAA; goodness-of-fit test; lognormal; maximum likelihood estimation; Weibull INTRODUCTION Poly(N-isopropylacrylamide) (PNIPAAm) is a ther- moresponsive polymer with a low critical solution temperature (LCST) around 32  C. 1 Because of its phase-transition property, PNIPAAm-based nano- particles have shown great potential applications in drug delivery, 2,3 sensing, 4,5 fabrication of photonic crystals, 6,7 nano templates, 8,9 and separation and pu- rification technologies. 10,11 For example, the fast responding property of the PNIPAAm nanoparticles make them useful for developing targeted and regu- lated drug delivery systems to multiple stimuli within a reasonable time. 12 The properties of nanoparticles and the perform- ance of the products made with nanosized precur- sors depend significantly on the shape of the particle-size distribution (PSD). This includes the broadness of the PSD, the modality, and the specific particle size covered by the PSD. The controlled adjustment of particle size is of great interest due to size-dependent physical and chemical properties of nanoparticles. In the pharmaceutical industry, for example, the PSD of the active pharmaceutical ingre- dients is one of the most important aspects of the dosage form that affect the effectiveness of drug release. 13 Besides, PSD may also affect the stability of the dosage and the absorption rate of an active intergradient. As a result, it is essential to control particle-size distribution in development of pharma- ceutical dosages. 14 The PSD of many nanoparticles in soil science, 15 environmental science, 16,17 biology, 18 and medical science 19 is often found to be lognormal. The earliest models of the lognormal distribution were based on Kolmogorov’s simple idea of stone cracking, where the relative change of the fragment volumes was taken to be stationary random variables. 20 A growth model, based on the same idea in a time-reversed fashion, was used later by Granqvist and Buhrman 20 in an attempt to explain the origin of lognormal dis- tributions of gas-evaporated nanoparticles. 21,22 Most of these models are based on coagulation theory developed by Smoluchowsky. 23 The Smoluchowsky model deals with a closed system where an initially large number of small particles meet and coagulate. As time passes, the mean particle size increases and the system gradually runs out of small particles. Kiss et al. 24 proposed a new approach to the origin of lognormal size distribution of nanoparticles based on residence time, where particle growth occurs dur- ing transport through a growth zone due to diffu- sion and draft. It needs to be pointed out that the lognormal distribution is often postulated in many analytical and numerical models, and the system is forced to stay in the lognormal state. On the other hand, the Weibull distribution, a mixed Weibull and lognormal distribution, and a segmented distribution have been found to better describe the particle size distribution in many systems. 25 Journal of Applied Polymer Science, Vol. 111, 2584–2589 (2009) V V C 2008 Wiley Periodicals, Inc. Correspondence to: Q. Wu (qwu@agcenter.lsu.edu). Contract grant sponsor: Louisiana Board of Regents Industrial Tie Subprogram; contract grant number: LEQSF(2006-08)-RD-B-02. Contract grant sponsor: BAIT (LSU Ag Center).