# Quartz Enhanced Conductance Spectroscopy for Polymer Nano-Mechanical Thermal Analysis
## 1 Introduction  
The nanomechanics of polymer materials has become increasingly significant for advanced technological applications including the field of optics, electricity, acoustics, mechanics, and biomedicine [1]. In order to determine the mechanics of polymer materials, research using micro samples is a large challenge, especially in some special environments or experiments [2; 3; 4; 5; 6; 7]. In 2016, [PERSON] et al. presented a novel approach to achieve microscale stimuli-responsive deformation of Janus structures for polymer actuators [6]. In addition, nanogram-level biomaterials with a silk structure have also been widely applied in many fields such as tissue engineering, drug delivery, electronic, and optical devices [7; 8; 9; 10].  
The melting temperature (\(T_{m}\)), which is the temperature at which one material can coexist and balance in a solid-liquid two phase, is one of the basic parameters to characterize the physicochemical properties of a crystal [11; 12]. The \(T_{m}\) of polymers is usually not a constant value since there are two factors that have a great impact on the \(T_{m}\) pressure and impurity [12]. Under a certain pressure, the temperature deviation from early fusion to the melt is not more than 0.5-1 \({}^{\circ}\)C [11; 13]. However, the \(T_{m}\) will change while the material is mixed with impurities. Therefore, the \(T_{m}\) determination is also the basic means to identify material purity [12].  
In the past decades, thermometry-based \(T_{m}\) determination has been developed and reported. Capillary melting point measurement is one of the conventional approaches to determine the \(T_{m}\)[14; 15; 16]. In this method, the powder samples are placed in the capillary tube with a temperature increment of 1 \({}^{\circ}\)C/min and the \(T_{m}\) corresponds to the temperature at which the powder samples in the tube begin to fall, and small droplets appear. Differential scanning calorimetry (DSC) is also an alternative and accurate technique for determining the \(T_{m}\)[17; 18; 19; 20; 21]. The samples are heated to 120 \({}^{\circ}\)C and the temperature is maintained for 2 h, then the nitrogen gas is passed over for dozens of minutes and a temperature increase rate at -10 \({}^{\circ}\)C/min is kept until the waxes have melt. The endothermic peak is shown in the DSC curve, and the melting point of samples is obtained accordingly. [PERSON] et al. measured the melting point and enthalpy of wax by means of the DSC method [18]. A polarized optical microscope (POM) was also used for \(T_{m}\) measurement of polymers [20; 21; 22]. With the light beam going into the crystal material, a double refraction phenomenon appears due to the anisotropy effect of the crystal. Heating the samples at a constant temperature rise rate, the melting of the sample and the disappearance of the birefringence phenomenon determines the \(T_{m}\).  
In this paper, we proposed a fast and convenient method to determine the polymer \(T_{m}\) based on a quartz tuning fork (QTF), which was characterized by the features of small volume but femto-Newton level force sensing [23; 24]. Quartz is a kind of material which has low internal losses, therefore the \(Q\) factor of a QTF is extremely high, usually -100,000 in vacuum and -10,000 in the atmosphere [25; 26; 27; 28; 29; 30]. The QTF can be used to detect the trace gas upon absorbing the excitation laser or to determine the inter-layer friction in multiwall carbon nanotubes [31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42]. Recently, quartz-enhanced conductance spectroscopy (QECS) based on a QTF was developed for analyzing the nanomechanical behaviors of polymers near the glass transition temperature [25]. In this work, the thermodynamics of three of the most commonly used polymers, namely, polymethyl methacrylate (PMMA), high-density polyethylene (HDPE), and disproportionated rosin (DPR) were analyzed in order to determine the \(T_{m}\) with the sample requirement of a few nanograms.