The SPR is an optical phenomenon related to a charge density oscillation at the interface between two materials which have the real parts of their dielectric constant of opposite sign [5]. The interaction of light and surface plasmon can be investigated using Fresnel reflection theory. Now, we assume the metal layer is sandwiched between prism and dielectric layer (biodiesel sample) and the incident wave is in the y-z plan so the amplitude of reflected light A_r can be expressed as: A r = r 123 A iwhere A_i is the amplitude of the incident light, and r₁₂₃ is the amplitude reflection coefficient which depends on thickness (t) as follows: (1) r 123 = r 12 + r 23   exp ( 2 ik 2 x t ) 1 + r 12   exp ( 2 ik 2 x t )where r₁₂, r₂₃ and k_2x are the reflection coefficient of metal dielectric, the reflection coefficient of glass metal and the phase constant [6], respectively. The k_ix and k_jx are (2) k ix = ( 2 π λ ) 2 ε i − k z 2 ,       k jx = ( 2 π λ ) 2 ε j − k z 2Where the k_z is the propagation constant ( 2 π λ n p   sin θ 2), and r_ij is (3) r ij = ε j k ix − ε i k jx ε j k ix + ε i k jx ,       i , j = 1 , 2 , 3The reflectivity is R = |r₁₂₃|².

The condition of resonance depends on the refractive index of gold and the sample [6] as follows: (4) n p   sin θ R = ( n 1 2 n 2 2 ) / ( n 1 2 + n 2 2 )where θ_R, n_p, n₁ and n₂ are the resonance angle, refractive indices of the prism, gold layer and sample, respectively. The refractive index of the sample is (5) n 2 = ( n 1 2 n p 2   sin 2 θ R ) / ( n 1 2 − n p 2   sin 2 θ R )

If A is the angle of the prism and θ₁ is the angle of incidence of the light beam directed to the prism, the angle of incidence on the metal layer is obtained as follows [7]: (6) θ 2 = A − arcsin ( ( n air / n p ) sin θ 1 )where n_air is the refractive index of air.

The reflectivity is a function of refractive index of sample, refractive index and thickness of gold layer. When the thickness and optical parameters of the gold layer are known, the angle of incidence at the interface between the prism and the gold layer is obtained from Equation (6). The refractive index and resonance angle of the sample will be found by minimizing the sum [8] (7) Γ = ∑ θ [ R Exp ( θ 2 , n 2 ) − R Theory ( θ 2 , n 2 ) ]where R_Exp and R_Theory are the experimental and theoretical reflectivity, respectively. The reflectivity is a function of angle and wavelength.

The photopyroelectric (PPE) technique was used to measure the thermal diffusivity of winter grade and normal grade palm oil biodiesel. In the low frequency (modulated radiation) regime, the thermal wave penetrates into the sample, and the sensor gives rise to a pyroelectric signal. The sample becomes thermally thick and the pyroelectric (PE) signal V(f) decreases exponentially with increasing modulation of the frequency. The decay rate (V) is determined by the thickness and thermal diffusivity of the sample. (8) V ( f ) = V 0   exp [ − ( 1 + i ) π f α L ] (9) L n | V ( f ) | = [ L n | V 0 | − π α L f ]where V(f) is the complex PE signal, V is its amplitude factor, and f is the modulation frequency. L, α are the thickness of sample and thermal diffusivity, respectively. The frequency scan of the PE signal provides the direct and absolute measurement of the thermal diffusivity of the sample [9].

The setup in Figure 1 consists of a precision rotation stage, a high refractive index prism (ZF 52, n = 1.83956, A = 60°, Foctek), a photodiode, a polarizer, a chopper, a lock-in amplifier, a He-Ne laser (632.8 nm, model: R30990, Newport) and a flow cell. The rotation stage and the photodiode were controlled with a program that was written with Matlab. In this setup, the rotation stage was connected to a stepper motor. At first, the prism was adjusted to its starting point before being rotated up to 40° with increments of 0.016° step size [10]. At each step, the rotation stage momentarily stopped for the reflected light intensity off the gold layer to be registered by the photodiode, which was connected to the lock-in amplifier. In addition, the angle of incidence between the air and the prism (θ₁) is also registered.

All measurements were carried out with the biodiesel in direct contact with the gold layer. The thickness of the gold layer, which was deposited on the prism with sputtering coating, was 49 nm. In order to determine the optical parameters of the biodiesel samples, the SPR setup was calibrated using deionized water; hence, the optical parameters (n, k) of the gold layer were also obtained. The SPR experiment was repeated with He-Ne laser (594.1 nm Uniphase, model: 1675), He-Ne laser (543.5 nm, Uniphase, model: 1677) and diode laser (405 nm, Power Technology, model LDCU87870).

The PPE setup in Figure 2 consists of a pyroelectric sensor (Polyvinylidene Diflouride PVDF (MSI DT1-028K/L)), a diode laser (532 nm, 200 mw), a lock in amplifier, metal thin foil (50 μm) and a fluid cell. The laser beam impinges on the black-painted external face of thin metal foil. This face of metal foil absorbed the energy and converted it into heat. Thus, the thermal wave generated by the laser beam was transferred into the liquid. The pyroelectric sensor (52 μm) detected the signal which is very sensitive to small changes in the heat flux [11]. It was fixed to a perspex substrate, PE transducer and backing is in a thermally thick condition. Thus, the resulting thermal wave is independent of the other cell parameters. The electromagnetic noise was reduced by eliminating all the ground loops via proper grounding. The operating parameters are controlled through a computer equipped with adapted virtual instrument software that allows automatic data acquisition. The frequency range for the scan was 5 Hz to 40 Hz. The thermal diffusivity measurement was performed at room temperature (∼20 °C). A careful calibration of the experimental setup and procedure was done and verified by measuring the thermal diffusivity of water (standard), prior to carrying out the actual measurements.

The winter grade biodiesel and normal grade biodiesel were analyzed by gas chromatography (GC). In this experiment, the fatty acid composition of methyl esters was determined using PerkinElmer GC-FID (Auto system XL, Shelton, CT, USA). The GC oven was kept at 140 °C and the helium gas was flowed in the fused silica column. Sodium methylate (0.3 mL) and hexane (1.0 mL) were added to 0.03 g of sample. The mixture was injected into GC with split ratio of 1:100.

The samples were tested with Fourier Transform Infrared Spectroscopy (FTIR) model Elmer 1725X. The spectrum from 1000 to 4000 cm⁻¹ was registered.